Ma, Wenjun; Sun, Liangliang Simultaneous recovery of two time-dependent coefficients in a multi-term time-fractional diffusion equation. (English) Zbl 07804034 Comput. Methods Appl. Math. 24, No. 1, 59-83 (2024). MSC: 35R30 35R25 35R11 65M30 PDFBibTeX XMLCite \textit{W. Ma} and \textit{L. Sun}, Comput. Methods Appl. Math. 24, No. 1, 59--83 (2024; Zbl 07804034) Full Text: DOI
Sun, Liangliang; Wang, Yuxin; Chang, Maoli A fractional-order quasi-reversibility method to a backward problem for the multi-term time-fractional diffusion equation. (English) Zbl 07788924 Taiwanese J. Math. 27, No. 6, 1185-1210 (2023). MSC: 65L08 35R30 35R25 65M30 PDFBibTeX XMLCite \textit{L. Sun} et al., Taiwanese J. Math. 27, No. 6, 1185--1210 (2023; Zbl 07788924) Full Text: DOI
Pskhu, Arsen Transmutation operators intertwining first-order and distributed-order derivatives. (English) Zbl 07785683 Bol. Soc. Mat. Mex., III. Ser. 29, No. 3, Paper No. 93, 17 p. (2023). MSC: 35R11 26A33 34A08 34A25 PDFBibTeX XMLCite \textit{A. Pskhu}, Bol. Soc. Mat. Mex., III. Ser. 29, No. 3, Paper No. 93, 17 p. (2023; Zbl 07785683) Full Text: DOI
Kian, Yavar Equivalence of definitions of solutions for some class of fractional diffusion equations. (English) Zbl 07785050 Math. Nachr. 296, No. 12, 5617-5645 (2023). MSC: 35R11 35B30 35K20 35R05 PDFBibTeX XMLCite \textit{Y. Kian}, Math. Nachr. 296, No. 12, 5617--5645 (2023; Zbl 07785050) Full Text: DOI arXiv
Eftekhari, Tahereh; Rashidinia, Jalil A new operational vector approach for time-fractional subdiffusion equations of distributed order based on hybrid functions. (English) Zbl 07781131 Math. Methods Appl. Sci. 46, No. 1, 388-407 (2023). MSC: 35R11 65N35 PDFBibTeX XMLCite \textit{T. Eftekhari} and \textit{J. Rashidinia}, Math. Methods Appl. Sci. 46, No. 1, 388--407 (2023; Zbl 07781131) Full Text: DOI
Ferrás, Luís L.; Morgado, M. Luísa; Rebelo, Magda A generalised distributed-order Maxwell model. (English) Zbl 07781130 Math. Methods Appl. Sci. 46, No. 1, 368-387 (2023). MSC: 76A10 44A10 PDFBibTeX XMLCite \textit{L. L. Ferrás} et al., Math. Methods Appl. Sci. 46, No. 1, 368--387 (2023; Zbl 07781130) Full Text: DOI arXiv
Yu, Qiang; Turner, Ian; Liu, Fawang; Moroney, Timothy A study of distributed-order time fractional diffusion models with continuous distribution weight functions. (English) Zbl 07779715 Numer. Methods Partial Differ. Equations 39, No. 1, 383-420 (2023). MSC: 65M06 65M12 65D32 44A10 35B40 PDFBibTeX XMLCite \textit{Q. Yu} et al., Numer. Methods Partial Differ. Equations 39, No. 1, 383--420 (2023; Zbl 07779715) Full Text: DOI
Chen, Xuejuan; Chen, Jinghua; Liu, Fawang; Sun, Zhi-zhong A fourth-order accurate numerical method for the distributed-order Riesz space fractional diffusion equation. (English) Zbl 07776962 Numer. Methods Partial Differ. Equations 39, No. 2, 1266-1286 (2023). MSC: 65-XX 35-XX PDFBibTeX XMLCite \textit{X. Chen} et al., Numer. Methods Partial Differ. Equations 39, No. 2, 1266--1286 (2023; Zbl 07776962) Full Text: DOI
Kian, Yavar; Soccorsi, Éric Solving time-fractional diffusion equations with a singular source term. (English) Zbl 1526.35290 Inverse Probl. 39, No. 12, Article ID 125005, 12 p. (2023). MSC: 35R11 35R30 PDFBibTeX XMLCite \textit{Y. Kian} and \textit{É. Soccorsi}, Inverse Probl. 39, No. 12, Article ID 125005, 12 p. (2023; Zbl 1526.35290) Full Text: DOI arXiv
Ferrás, L. L.; Rebelo, M.; Morgado, M. L. The role of the weight function in the generalised distributed-order Maxwell model: the case of a distributed-springpot and a dashpot. (English) Zbl 1525.76006 Appl. Math. Modelling 122, 844-860 (2023). MSC: 76A10 35R11 PDFBibTeX XMLCite \textit{L. L. Ferrás} et al., Appl. Math. Modelling 122, 844--860 (2023; Zbl 1525.76006) Full Text: DOI
Derakhshan, Mohammad Hossein Stability analysis of difference-Legendre spectral method for two-dimensional Riesz space distributed-order diffusion-wave model. (English) Zbl 07731302 Comput. Math. Appl. 144, 150-163 (2023). MSC: 65-XX 35R11 65M12 26A33 65M06 65M60 PDFBibTeX XMLCite \textit{M. H. Derakhshan}, Comput. Math. Appl. 144, 150--163 (2023; Zbl 07731302) Full Text: DOI
Ansari, Alireza; Derakhshan, Mohammad Hossein On spectral polar fractional Laplacian. (English) Zbl 07700841 Math. Comput. Simul. 206, 636-663 (2023). MSC: 65-XX 35-XX PDFBibTeX XMLCite \textit{A. Ansari} and \textit{M. H. Derakhshan}, Math. Comput. Simul. 206, 636--663 (2023; Zbl 07700841) Full Text: DOI
Tuan, Tran Van Stability and regularity in inverse source problem for generalized subdiffusion equation perturbed by locally Lipschitz sources. (English) Zbl 1510.35388 Z. Angew. Math. Phys. 74, No. 2, Paper No. 65, 25 p. (2023). MSC: 35R11 35B40 35C15 35R09 45D05 45K05 PDFBibTeX XMLCite \textit{T. Van Tuan}, Z. Angew. Math. Phys. 74, No. 2, Paper No. 65, 25 p. (2023; Zbl 1510.35388) Full Text: DOI
Kumar, Yashveer; Srivastava, Nikhil; Singh, Aman; Singh, Vineet Kumar Wavelets based computational algorithms for multidimensional distributed order fractional differential equations with nonlinear source term. (English) Zbl 07648417 Comput. Math. Appl. 132, 73-103 (2023). MSC: 65M70 26A33 34A08 65T60 65L60 65L05 PDFBibTeX XMLCite \textit{Y. Kumar} et al., Comput. Math. Appl. 132, 73--103 (2023; Zbl 07648417) Full Text: DOI
Vieira, Nelson; Rodrigues, M. Manuela; Ferreira, Milton Time-fractional telegraph equation of distributed order in higher dimensions with Hilfer fractional derivatives. (English) Zbl 1512.35641 Electron. Res. Arch. 30, No. 10, 3595-3631 (2022). MSC: 35R11 35L15 PDFBibTeX XMLCite \textit{N. Vieira} et al., Electron. Res. Arch. 30, No. 10, 3595--3631 (2022; Zbl 1512.35641) Full Text: DOI
Garra, R.; Consiglio, A.; Mainardi, F. A note on a modified fractional Maxwell model. (English) Zbl 1507.74065 Chaos Solitons Fractals 163, Article ID 112544, 5 p. (2022). MSC: 74B05 74D05 74L10 76A10 26A33 35R11 33E12 PDFBibTeX XMLCite \textit{R. Garra} et al., Chaos Solitons Fractals 163, Article ID 112544, 5 p. (2022; Zbl 1507.74065) Full Text: DOI arXiv
Vitali, S.; Paradisi, P.; Pagnini, G. Anomalous diffusion originated by two Markovian hopping-trap mechanisms. (English) Zbl 1506.60111 J. Phys. A, Math. Theor. 55, No. 22, Article ID 224012, 26 p. (2022). MSC: 60K50 PDFBibTeX XMLCite \textit{S. Vitali} et al., J. Phys. A, Math. Theor. 55, No. 22, Article ID 224012, 26 p. (2022; Zbl 1506.60111) Full Text: DOI arXiv
Awad, Emad; Metzler, Ralf Closed-form multi-dimensional solutions and asymptotic behaviours for subdiffusive processes with crossovers. II: Accelerating case. (English) Zbl 1506.35259 J. Phys. A, Math. Theor. 55, No. 20, Article ID 205003, 29 p. (2022). MSC: 35R11 60K50 PDFBibTeX XMLCite \textit{E. Awad} and \textit{R. Metzler}, J. Phys. A, Math. Theor. 55, No. 20, Article ID 205003, 29 p. (2022; Zbl 1506.35259) Full Text: DOI
Ansari, Alireza; Derakhshan, Mohammad Hossein; Askari, Hassan Distributed order fractional diffusion equation with fractional Laplacian in axisymmetric cylindrical configuration. (English) Zbl 1500.35290 Commun. Nonlinear Sci. Numer. Simul. 113, Article ID 106590, 14 p. (2022). MSC: 35R11 26A33 35A08 35C15 44A10 44A20 PDFBibTeX XMLCite \textit{A. Ansari} et al., Commun. Nonlinear Sci. Numer. Simul. 113, Article ID 106590, 14 p. (2022; Zbl 1500.35290) Full Text: DOI
Janno, Jaan; Kasemets, Kairi; Kinash, Nataliia Inverse problem to identify a space-dependent diffusivity coefficient in a generalized subdiffusion equation from final data. (English) Zbl 1487.35447 Proc. Est. Acad. Sci. 71, No. 1, 3-15 (2022). MSC: 35R30 35K20 35R11 PDFBibTeX XMLCite \textit{J. Janno} et al., Proc. Est. Acad. Sci. 71, No. 1, 3--15 (2022; Zbl 1487.35447) Full Text: DOI
Awad, Emad; Sandev, Trifce; Metzler, Ralf; Chechkin, Aleksei Closed-form multi-dimensional solutions and asymptotic behaviors for subdiffusive processes with crossovers. I: Retarding case. (English) Zbl 1506.35260 Chaos Solitons Fractals 152, Article ID 111357, 18 p. (2021). MSC: 35R11 60K50 PDFBibTeX XMLCite \textit{E. Awad} et al., Chaos Solitons Fractals 152, Article ID 111357, 18 p. (2021; Zbl 1506.35260) Full Text: DOI
Liu, Xingguo; Yang, Xuehua; Zhang, Haixiang; Liu, Yanling Discrete singular convolution for fourth-order multi-term time fractional equation. (English) Zbl 07534877 Tbil. Math. J. 14, No. 2, 1-16 (2021). MSC: 65-XX 35K61 65N12 65N30 PDFBibTeX XMLCite \textit{X. Liu} et al., Tbil. Math. J. 14, No. 2, 1--16 (2021; Zbl 07534877) Full Text: DOI
Pourbabaee, Marzieh; Saadatmandi, Abbas The construction of a new operational matrix of the distributed-order fractional derivative using Chebyshev polynomials and its applications. (English) Zbl 1491.65113 Int. J. Comput. Math. 98, No. 11, 2310-2329 (2021). MSC: 65M70 65D32 65M15 41A50 26A33 35R11 PDFBibTeX XMLCite \textit{M. Pourbabaee} and \textit{A. Saadatmandi}, Int. J. Comput. Math. 98, No. 11, 2310--2329 (2021; Zbl 1491.65113) Full Text: DOI
Chen, An Two efficient Galerkin finite element methods for the modified anomalous subdiffusion equation. (English) Zbl 1480.65249 Int. J. Comput. Math. 98, No. 9, 1834-1851 (2021). MSC: 65M60 65M12 65M15 PDFBibTeX XMLCite \textit{A. Chen}, Int. J. Comput. Math. 98, No. 9, 1834--1851 (2021; Zbl 1480.65249) Full Text: DOI
López, José L.; Pagola, Pedro J.; Palacios, Pablo Series representations of the Volterra function and the Fransén-Robinson constant. (English) Zbl 1499.33087 J. Approx. Theory 272, Article ID 105641, 14 p. (2021). Reviewer: Faitori Omer Salem (Tripoli) MSC: 33E20 41A58 PDFBibTeX XMLCite \textit{J. L. López} et al., J. Approx. Theory 272, Article ID 105641, 14 p. (2021; Zbl 1499.33087) Full Text: DOI
Samiee, Mehdi; Kharazmi, Ehsan; Meerschaert, Mark M.; Zayernouri, Mohsen A unified Petrov-Galerkin spectral method and fast solver for distributed-order partial differential equations. (English) Zbl 1476.65272 Commun. Appl. Math. Comput. 3, No. 1, 61-90 (2021). MSC: 65M70 35Q49 58C40 65M12 65M15 PDFBibTeX XMLCite \textit{M. Samiee} et al., Commun. Appl. Math. Comput. 3, No. 1, 61--90 (2021; Zbl 1476.65272) Full Text: DOI
Vieira, N.; Rodrigues, M. M.; Ferreira, M. Time-fractional telegraph equation of distributed order in higher dimensions. (English) Zbl 1471.35313 Commun. Nonlinear Sci. Numer. Simul. 102, Article ID 105925, 32 p. (2021). MSC: 35R11 35L20 26A33 33C60 35C15 35A22 35S10 PDFBibTeX XMLCite \textit{N. Vieira} et al., Commun. Nonlinear Sci. Numer. Simul. 102, Article ID 105925, 32 p. (2021; Zbl 1471.35313) Full Text: DOI
Liu, Wei; Röckner, Michael; Luís da Silva, José Strong dissipativity of generalized time-fractional derivatives and quasi-linear (stochastic) partial differential equations. (English) Zbl 1469.35227 J. Funct. Anal. 281, No. 8, Article ID 109135, 34 p. (2021). MSC: 35R11 60H15 35K59 76S05 26A33 45K05 35K92 PDFBibTeX XMLCite \textit{W. Liu} et al., J. Funct. Anal. 281, No. 8, Article ID 109135, 34 p. (2021; Zbl 1469.35227) Full Text: DOI arXiv
Liu, J. J.; Sun, C. L.; Yamamoto, M. Recovering the weight function in distributed order fractional equation from interior measurement. (English) Zbl 1486.65154 Appl. Numer. Math. 168, 84-103 (2021). MSC: 65M32 65M06 65N06 65K10 49N45 35B65 26A33 35R11 PDFBibTeX XMLCite \textit{J. J. Liu} et al., Appl. Numer. Math. 168, 84--103 (2021; Zbl 1486.65154) Full Text: DOI
Bazhlekova, Emilia Completely monotone multinomial Mittag-Leffler type functions and diffusion equations with multiple time-derivatives. (English) Zbl 1499.35618 Fract. Calc. Appl. Anal. 24, No. 1, 88-111 (2021). MSC: 35R11 33E12 26A33 35E05 35K05 PDFBibTeX XMLCite \textit{E. Bazhlekova}, Fract. Calc. Appl. Anal. 24, No. 1, 88--111 (2021; Zbl 1499.35618) Full Text: DOI
Sun, L. L.; Li, Y. S.; Zhang, Y. Simultaneous inversion of the potential term and the fractional orders in a multi-term time-fractional diffusion equation. (English) Zbl 1462.35469 Inverse Probl. 37, No. 5, Article ID 055007, 26 p. (2021). MSC: 35R30 35R11 35K20 65M32 26A33 PDFBibTeX XMLCite \textit{L. L. Sun} et al., Inverse Probl. 37, No. 5, Article ID 055007, 26 p. (2021; Zbl 1462.35469) Full Text: DOI
Capała, Karol; Dybiec, Bartłomiej Deterministic force-free resonant activation. (English) Zbl 07330573 J. Stat. Mech. Theory Exp. 2021, No. 2, Article ID 023203, 16 p. (2021). MSC: 82-XX PDFBibTeX XMLCite \textit{K. Capała} and \textit{B. Dybiec}, J. Stat. Mech. Theory Exp. 2021, No. 2, Article ID 023203, 16 p. (2021; Zbl 07330573) Full Text: DOI arXiv
Sun, Chunlong; Liu, Jijun An inverse source problem for distributed order time-fractional diffusion equation. (English) Zbl 1469.35263 Inverse Probl. 36, No. 5, Article ID 055008, 30 p. (2020). MSC: 35R30 35K20 35R11 65M32 PDFBibTeX XMLCite \textit{C. Sun} and \textit{J. Liu}, Inverse Probl. 36, No. 5, Article ID 055008, 30 p. (2020; Zbl 1469.35263) Full Text: DOI
Hashan, Mahamudul; Jahan, Labiba Nusrat; Tareq-Uz-Zaman; Imtiaz, Syed; Hossain, M. Enamul Modelling of fluid flow through porous media using memory approach: a review. (English) Zbl 1510.76158 Math. Comput. Simul. 177, 643-673 (2020). MSC: 76S05 PDFBibTeX XMLCite \textit{M. Hashan} et al., Math. Comput. Simul. 177, 643--673 (2020; Zbl 1510.76158) Full Text: DOI
Beghin, Luisa; Caputo, Michele Commutative and associative properties of the Caputo fractional derivative and its generalizing convolution operator. (English) Zbl 1451.26007 Commun. Nonlinear Sci. Numer. Simul. 89, Article ID 105338, 6 p. (2020). Reviewer: Kai Diethelm (Schweinfurt) MSC: 26A33 26A06 60G51 PDFBibTeX XMLCite \textit{L. Beghin} and \textit{M. Caputo}, Commun. Nonlinear Sci. Numer. Simul. 89, Article ID 105338, 6 p. (2020; Zbl 1451.26007) Full Text: DOI
Van Bockstal, Karel Existence and uniqueness of a weak solution to a non-autonomous time-fractional diffusion equation (of distributed order). (English) Zbl 1450.35282 Appl. Math. Lett. 109, Article ID 106540, 7 p. (2020). MSC: 35R11 35K20 PDFBibTeX XMLCite \textit{K. Van Bockstal}, Appl. Math. Lett. 109, Article ID 106540, 7 p. (2020; Zbl 1450.35282) Full Text: DOI Link
Awad, Emad; Metzler, Ralf Crossover dynamics from superdiffusion to subdiffusion: models and solutions. (English) Zbl 1439.35519 Fract. Calc. Appl. Anal. 23, No. 1, 55-102 (2020). MSC: 35R11 35K57 33E12 PDFBibTeX XMLCite \textit{E. Awad} and \textit{R. Metzler}, Fract. Calc. Appl. Anal. 23, No. 1, 55--102 (2020; Zbl 1439.35519) Full Text: DOI
Li, Zhiyuan; Fujishiro, Kenichi; Li, Gongsheng Uniqueness in the inversion of distributed orders in ultraslow diffusion equations. (English) Zbl 1430.35257 J. Comput. Appl. Math. 369, Article ID 112564, 13 p. (2020). MSC: 35R11 35R30 44A10 PDFBibTeX XMLCite \textit{Z. Li} et al., J. Comput. Appl. Math. 369, Article ID 112564, 13 p. (2020; Zbl 1430.35257) Full Text: DOI arXiv
Li, Lang; Liu, Fawang; Feng, Libo; Turner, Ian A Galerkin finite element method for the modified distributed-order anomalous sub-diffusion equation. (English) Zbl 1440.65142 J. Comput. Appl. Math. 368, Article ID 112589, 18 p. (2020). MSC: 65M60 65N30 65M06 65D30 65M12 65M15 26A33 35R11 PDFBibTeX XMLCite \textit{L. Li} et al., J. Comput. Appl. Math. 368, Article ID 112589, 18 p. (2020; Zbl 1440.65142) Full Text: DOI
Nandal, Sarita; Pandey, Dwijendra Narain Numerical solution of non-linear fourth order fractional sub-diffusion wave equation with time delay. (English) Zbl 1433.65163 Appl. Math. Comput. 369, Article ID 124900, 14 p. (2020). MSC: 65M06 65M12 35R11 PDFBibTeX XMLCite \textit{S. Nandal} and \textit{D. N. Pandey}, Appl. Math. Comput. 369, Article ID 124900, 14 p. (2020; Zbl 1433.65163) Full Text: DOI
Awad, Emad On the time-fractional Cattaneo equation of distributed order. (English) Zbl 1514.35454 Physica A 518, 210-233 (2019). MSC: 35R11 PDFBibTeX XMLCite \textit{E. Awad}, Physica A 518, 210--233 (2019; Zbl 1514.35454) Full Text: DOI
Kinash, Nataliia; Janno, Jaan Inverse problems for a generalized subdiffusion equation with final overdetermination. (English) Zbl 1472.35456 Math. Model. Anal. 24, No. 2, 236-262 (2019). MSC: 35R30 35R11 PDFBibTeX XMLCite \textit{N. Kinash} and \textit{J. Janno}, Math. Model. Anal. 24, No. 2, 236--262 (2019; Zbl 1472.35456) Full Text: DOI
Liang, Yingjie; Chen, Wen; Xu, Wei; Sun, HongGuang Distributed order Hausdorff derivative diffusion model to characterize non-Fickian diffusion in porous media. (English) Zbl 1464.82017 Commun. Nonlinear Sci. Numer. Simul. 70, 384-393 (2019). MSC: 82C70 PDFBibTeX XMLCite \textit{Y. Liang} et al., Commun. Nonlinear Sci. Numer. Simul. 70, 384--393 (2019; Zbl 1464.82017) Full Text: DOI arXiv
Salehi, Rezvan Two implicit meshless finite point schemes for the two-dimensional distributed-order fractional equation. (English) Zbl 1434.65209 Comput. Methods Appl. Math. 19, No. 4, 813-831 (2019). MSC: 65M70 65M12 65M15 35R11 60G22 PDFBibTeX XMLCite \textit{R. Salehi}, Comput. Methods Appl. Math. 19, No. 4, 813--831 (2019; Zbl 1434.65209) Full Text: DOI
Zahra, W. K.; Nasr, M. A.; Van Daele, M. Exponentially fitted methods for solving time fractional nonlinear reaction-diffusion equation. (English) Zbl 1429.65206 Appl. Math. Comput. 358, 468-490 (2019). MSC: 65M06 65M12 35R11 35K57 PDFBibTeX XMLCite \textit{W. K. Zahra} et al., Appl. Math. Comput. 358, 468--490 (2019; Zbl 1429.65206) Full Text: DOI
Abdelkawy, M. A.; Lopes, António M.; Zaky, M. A. Shifted fractional Jacobi spectral algorithm for solving distributed order time-fractional reaction-diffusion equations. (English) Zbl 1438.65244 Comput. Appl. Math. 38, No. 2, Paper No. 81, 21 p. (2019). MSC: 65M70 74S25 26A33 35R11 33C45 65M12 65M15 PDFBibTeX XMLCite \textit{M. A. Abdelkawy} et al., Comput. Appl. Math. 38, No. 2, Paper No. 81, 21 p. (2019; Zbl 1438.65244) Full Text: DOI
Wei, Leilei; Liu, Lijie; Sun, Huixia Stability and convergence of a local discontinuous Galerkin method for the fractional diffusion equation with distributed order. (English) Zbl 1422.65271 J. Appl. Math. Comput. 59, No. 1-2, 323-341 (2019). MSC: 65M60 65M12 65M06 35S10 65M15 35R11 PDFBibTeX XMLCite \textit{L. Wei} et al., J. Appl. Math. Comput. 59, No. 1--2, 323--341 (2019; Zbl 1422.65271) Full Text: DOI
Huang, Xinchi; Li, Zhiyuan; Yamamoto, Masahiro Carleman estimates for the time-fractional advection-diffusion equations and applications. (English) Zbl 1418.35050 Inverse Probl. 35, No. 4, Article ID 045003, 36 p. (2019). MSC: 35B45 35R30 35R11 35K15 PDFBibTeX XMLCite \textit{X. Huang} et al., Inverse Probl. 35, No. 4, Article ID 045003, 36 p. (2019; Zbl 1418.35050) Full Text: DOI arXiv
Hernández-Hernández, M. E.; Kolokoltsov, V. N. Probabilistic solutions to nonlinear fractional differential equations of generalized Caputo and Riemann-Liouville type. (English) Zbl 1498.60284 Stochastics 90, No. 2, 224-255 (2018). MSC: 60H30 60G22 26A33 34A08 PDFBibTeX XMLCite \textit{M. E. Hernández-Hernández} and \textit{V. N. Kolokoltsov}, Stochastics 90, No. 2, 224--255 (2018; Zbl 1498.60284) Full Text: DOI
Želi, Velibor; Zorica, Dušan Analytical and numerical treatment of the heat conduction equation obtained via time-fractional distributed-order heat conduction law. (English) Zbl 1514.80002 Physica A 492, 2316-2335 (2018). MSC: 80A05 35Q79 35R11 80M20 PDFBibTeX XMLCite \textit{V. Želi} and \textit{D. Zorica}, Physica A 492, 2316--2335 (2018; Zbl 1514.80002) Full Text: DOI arXiv
Butko, Yana A. Chernoff approximation for semigroups generated by killed Feller processes and Feynman formulae for time-fractional Fokker-Planck-Kolmogorov equations. (English) Zbl 1422.35162 Fract. Calc. Appl. Anal. 21, No. 5, 1203-1237 (2018). MSC: 35R11 35Q84 47D06 47D07 35K20 60J75 PDFBibTeX XMLCite \textit{Y. A. Butko}, Fract. Calc. Appl. Anal. 21, No. 5, 1203--1237 (2018; Zbl 1422.35162) Full Text: DOI arXiv
Abdelkawy, M. A. A collocation method based on Jacobi and fractional order Jacobi basis functions for multi-dimensional distributed-order diffusion equations. (English) Zbl 1461.65243 Int. J. Nonlinear Sci. Numer. Simul. 19, No. 7-8, 781-792 (2018). MSC: 65M70 35K58 35R11 PDFBibTeX XMLCite \textit{M. A. Abdelkawy}, Int. J. Nonlinear Sci. Numer. Simul. 19, No. 7--8, 781--792 (2018; Zbl 1461.65243) Full Text: DOI
Liu, Quanzhen; Mu, Shanjun; Liu, Qingxia; Liu, Baoquan; Bi, Xiaolei; Zhuang, Pinghui; Li, Bochen; Gao, Jian An RBF based meshless method for the distributed order time fractional advection-diffusion equation. (English) Zbl 1403.65096 Eng. Anal. Bound. Elem. 96, 55-63 (2018). MSC: 65M70 35R11 PDFBibTeX XMLCite \textit{Q. Liu} et al., Eng. Anal. Bound. Elem. 96, 55--63 (2018; Zbl 1403.65096) Full Text: DOI
Yang, Xuehua; Zhang, Haixiang; Xu, Da WSGD-OSC scheme for two-dimensional distributed order fractional reaction-diffusion equation. (English) Zbl 1397.65210 J. Sci. Comput. 76, No. 3, 1502-1520 (2018). MSC: 65M70 65M12 65M15 35R11 PDFBibTeX XMLCite \textit{X. Yang} et al., J. Sci. Comput. 76, No. 3, 1502--1520 (2018; Zbl 1397.65210) Full Text: DOI
Zaky, Mahmoud A. A Legendre collocation method for distributed-order fractional optimal control problems. (English) Zbl 1392.35331 Nonlinear Dyn. 91, No. 4, 2667-2681 (2018). MSC: 35R11 65M70 65K15 93C20 PDFBibTeX XMLCite \textit{M. A. Zaky}, Nonlinear Dyn. 91, No. 4, 2667--2681 (2018; Zbl 1392.35331) Full Text: DOI
Chidouh, Amar; Guezane-Lakoud, Assia; Bebbouchi, Rachid; Bouaricha, Amor; Torres, Delfim F. M. Linear and nonlinear fractional Voigt models. (English) Zbl 1460.74011 Babiarz, Artur (ed.) et al., Theory and applications of non-integer order systems. Papers of the 8th conference on non-integer order calculus and its applications, Zakopane, Poland, September 20–21, 2016. Cham: Springer. Lect. Notes Electr. Eng. 407, 157-167 (2017). MSC: 74D05 74D10 74H20 26A33 PDFBibTeX XMLCite \textit{A. Chidouh} et al., Lect. Notes Electr. Eng. 407, 157--167 (2017; Zbl 1460.74011) Full Text: DOI arXiv
Li, Zhiyuan; Luchko, Yuri; Yamamoto, Masahiro Analyticity of solutions to a distributed order time-fractional diffusion equation and its application to an inverse problem. (English) Zbl 1409.35221 Comput. Math. Appl. 73, No. 6, 1041-1052 (2017). MSC: 35R11 35B65 35R30 PDFBibTeX XMLCite \textit{Z. Li} et al., Comput. Math. Appl. 73, No. 6, 1041--1052 (2017; Zbl 1409.35221) Full Text: DOI
Sandev, Trifce; Tomovski, Zivorad; Crnkovic, Bojan Generalized distributed order diffusion equations with composite time fractional derivative. (English) Zbl 1409.35227 Comput. Math. Appl. 73, No. 6, 1028-1040 (2017). MSC: 35R11 PDFBibTeX XMLCite \textit{T. Sandev} et al., Comput. Math. Appl. 73, No. 6, 1028--1040 (2017; Zbl 1409.35227) Full Text: DOI arXiv
Sandev, Trifce; Sokolov, Igor M.; Metzler, Ralf; Chechkin, Aleksei Beyond monofractional kinetics. (English) Zbl 1374.45016 Chaos Solitons Fractals 102, 210-217 (2017). MSC: 45K05 35R11 PDFBibTeX XMLCite \textit{T. Sandev} et al., Chaos Solitons Fractals 102, 210--217 (2017; Zbl 1374.45016) Full Text: DOI
Hernández-Hernández, M. E.; Kolokoltsov, V. N.; Toniazzi, L. Generalised fractional evolution equations of Caputo type. (English) Zbl 1374.34009 Chaos Solitons Fractals 102, 184-196 (2017). MSC: 34A08 34A12 60H30 34A05 PDFBibTeX XMLCite \textit{M. E. Hernández-Hernández} et al., Chaos Solitons Fractals 102, 184--196 (2017; Zbl 1374.34009) Full Text: DOI arXiv Link
Abbaszadeh, Mostafa; Dehghan, Mehdi An improved meshless method for solving two-dimensional distributed order time-fractional diffusion-wave equation with error estimate. (English) Zbl 1412.65131 Numer. Algorithms 75, No. 1, 173-211 (2017). MSC: 65M60 65M12 35R11 PDFBibTeX XMLCite \textit{M. Abbaszadeh} and \textit{M. Dehghan}, Numer. Algorithms 75, No. 1, 173--211 (2017; Zbl 1412.65131) Full Text: DOI
Rundell, W.; Zhang, Z. Fractional diffusion: recovering the distributed fractional derivative from overposed data. (English) Zbl 1372.35371 Inverse Probl. 33, No. 3, Article ID 035008, 27 p. (2017). MSC: 35R30 35R11 35K10 PDFBibTeX XMLCite \textit{W. Rundell} and \textit{Z. Zhang}, Inverse Probl. 33, No. 3, Article ID 035008, 27 p. (2017; Zbl 1372.35371) Full Text: DOI arXiv
Moslehi, Leila; Ansari, Alireza On \(M\)-Wright transforms and time-fractional diffusion equations. (English) Zbl 1365.35215 Integral Transforms Spec. Funct. 28, No. 2, 113-129 (2017). MSC: 35R11 26A33 35C15 44A10 PDFBibTeX XMLCite \textit{L. Moslehi} and \textit{A. Ansari}, Integral Transforms Spec. Funct. 28, No. 2, 113--129 (2017; Zbl 1365.35215) Full Text: DOI
Pimenov, V. G.; Hendy, A. S.; De Staelen, R. H. On a class of non-linear delay distributed order fractional diffusion equations. (English) Zbl 1357.65127 J. Comput. Appl. Math. 318, 433-443 (2017). MSC: 65M06 35K55 35R11 35R10 65M12 PDFBibTeX XMLCite \textit{V. G. Pimenov} et al., J. Comput. Appl. Math. 318, 433--443 (2017; Zbl 1357.65127) Full Text: DOI
Morgado, Maria Luísa; Rebelo, Magda; Ferrás, Luis L.; Ford, Neville J. Numerical solution for diffusion equations with distributed order in time using a Chebyshev collocation method. (English) Zbl 1357.65198 Appl. Numer. Math. 114, 108-123 (2017). MSC: 65M70 35K05 35R11 65M15 PDFBibTeX XMLCite \textit{M. L. Morgado} et al., Appl. Numer. Math. 114, 108--123 (2017; Zbl 1357.65198) Full Text: DOI Link
Wei, Song; Chen, Wen; Hon, Y. C. Characterizing time dependent anomalous diffusion process: a survey on fractional derivative and nonlinear models. (English) Zbl 1400.65047 Physica A 462, 1244-1251 (2016). MSC: 65M06 35R11 76R50 80A10 PDFBibTeX XMLCite \textit{S. Wei} et al., Physica A 462, 1244--1251 (2016; Zbl 1400.65047) Full Text: DOI
Hossain, M. Enamul Numerical investigation of memory-based diffusivity equation: the integro-differential equation. (English) Zbl 1448.65191 Arab. J. Sci. Eng. 41, No. 7, 2715-2729 (2016). MSC: 65N06 65R20 45K05 35R09 35R11 26A33 76S05 PDFBibTeX XMLCite \textit{M. E. Hossain}, Arab. J. Sci. Eng. 41, No. 7, 2715--2729 (2016; Zbl 1448.65191) Full Text: DOI
Gao, Guang-hua; Sun, Zhi-zhong Two alternating direction implicit difference schemes for two-dimensional distributed-order fractional diffusion equations. (English) Zbl 1373.65055 J. Sci. Comput. 66, No. 3, 1281-1312 (2016). Reviewer: Charis Harley (Johannesburg) MSC: 65M06 35K05 35R11 65M12 PDFBibTeX XMLCite \textit{G.-h. Gao} and \textit{Z.-z. Sun}, J. Sci. Comput. 66, No. 3, 1281--1312 (2016; Zbl 1373.65055) Full Text: DOI
Gao, Guang-hua; Sun, Zhi-zhong Two alternating direction implicit difference schemes for solving the two-dimensional time distributed-order wave equations. (English) Zbl 1372.65230 J. Sci. Comput. 69, No. 2, 506-531 (2016). Reviewer: Seenith Sivasundaram (Daytona Beach) MSC: 65M06 35L05 35R11 65M12 PDFBibTeX XMLCite \textit{G.-h. Gao} and \textit{Z.-z. Sun}, J. Sci. Comput. 69, No. 2, 506--531 (2016; Zbl 1372.65230) Full Text: DOI
Chidouh, Amar; Guezane-Lakoud, Assia; Bebbouchi, Rachid Positive solutions of the fractional relaxation equation using lower and upper solutions. (English) Zbl 1358.34009 Vietnam J. Math. 44, No. 4, 739-748 (2016). MSC: 34A08 34A12 33E12 47N20 PDFBibTeX XMLCite \textit{A. Chidouh} et al., Vietnam J. Math. 44, No. 4, 739--748 (2016; Zbl 1358.34009) Full Text: DOI
Morgado, Maria Luísa; Rebelo, Magda Chebyshev spectral approximation for diffusion equations with distributed order in time. (English) Zbl 1355.65138 Pinelas, Sandra (ed.) et al., Differential and difference equations with applications. ICDDEA, Amadora, Portugal, May 18–22, 2015. Selected contributions. Cham: Springer (ISBN 978-3-319-32855-3/hbk; 978-3-319-32857-7/ebook). Springer Proceedings in Mathematics & Statistics 164, 255-263 (2016). MSC: 65M70 35K05 35R11 PDFBibTeX XMLCite \textit{M. L. Morgado} and \textit{M. Rebelo}, Springer Proc. Math. Stat. 164, 255--263 (2016; Zbl 1355.65138) Full Text: DOI
Chen, Hu; Lü, Shujuan; Chen, Wenping Finite difference/spectral approximations for the distributed order time fractional reaction-diffusion equation on an unbounded domain. (English) Zbl 1349.65507 J. Comput. Phys. 315, 84-97 (2016). MSC: 65M70 65M15 35R11 35K57 PDFBibTeX XMLCite \textit{H. Chen} et al., J. Comput. Phys. 315, 84--97 (2016; Zbl 1349.65507) Full Text: DOI
Garrappa, Roberto; Mainardi, Francesco On Volterra functions and Ramanujan integrals. (English) Zbl 1342.45001 Analysis, München 36, No. 2, 89-105 (2016). MSC: 45D05 45E05 33E20 33E50 33F05 65D20 PDFBibTeX XMLCite \textit{R. Garrappa} and \textit{F. Mainardi}, Analysis, München 36, No. 2, 89--105 (2016; Zbl 1342.45001) Full Text: DOI arXiv
Gao, Guang-Hua; Sun, Zhi-Zhong Two unconditionally stable and convergent difference schemes with the extrapolation method for the one-dimensional distributed-order differential equations. (English) Zbl 1339.65115 Numer. Methods Partial Differ. Equations 32, No. 2, 591-615 (2016). MSC: 65M06 65M12 PDFBibTeX XMLCite \textit{G.-H. Gao} and \textit{Z.-Z. Sun}, Numer. Methods Partial Differ. Equations 32, No. 2, 591--615 (2016; Zbl 1339.65115) Full Text: DOI
Jin, Bangti; Lazarov, Raytcho; Sheen, Dongwoo; Zhou, Zhi Error estimates for approximations of distributed order time fractional diffusion with nonsmooth data. (English) Zbl 1333.65111 Fract. Calc. Appl. Anal. 19, No. 1, 69-93 (2016). Reviewer: Abdallah Bradji (Annaba) MSC: 65M60 35R11 65M15 PDFBibTeX XMLCite \textit{B. Jin} et al., Fract. Calc. Appl. Anal. 19, No. 1, 69--93 (2016; Zbl 1333.65111) Full Text: DOI arXiv
Li, Zhiyuan; Imanuvilov, Oleg Yu; Yamamoto, Masahiro Uniqueness in inverse boundary value problems for fractional diffusion equations. (English) Zbl 1332.35396 Inverse Probl. 32, No. 1, Article ID 015004, 16 p. (2016). MSC: 35R30 35R11 35A02 PDFBibTeX XMLCite \textit{Z. Li} et al., Inverse Probl. 32, No. 1, Article ID 015004, 16 p. (2016; Zbl 1332.35396) Full Text: DOI arXiv
Gao, Guang-hua; Sun, Zhi-zhong Two alternating direction implicit difference schemes with the extrapolation method for the two-dimensional distributed-order differential equations. (English) Zbl 1443.65124 Comput. Math. Appl. 69, No. 9, 926-948 (2015). MSC: 65M06 65M12 35R11 PDFBibTeX XMLCite \textit{G.-h. Gao} and \textit{Z.-z. Sun}, Comput. Math. Appl. 69, No. 9, 926--948 (2015; Zbl 1443.65124) Full Text: DOI
Guo, Gang; Chen, Bin; Zhao, Xinjun; Zhao, Fang; Wang, Quanmin First passage time distribution of a modified fractional diffusion equation in the semi-infinite interval. (English) Zbl 1400.35219 Physica A 433, 279-290 (2015). MSC: 35R11 60H10 PDFBibTeX XMLCite \textit{G. Guo} et al., Physica A 433, 279--290 (2015; Zbl 1400.35219) Full Text: DOI
Montseny, Emmanuel; Casenave, Céline Analysis, simulation and impedance operator of a nonlocal model of porous medium for acoustic control. (English) Zbl 1358.93119 J. Vib. Control 21, No. 5, 1012-1028 (2015). MSC: 93C80 76Q05 74H45 93E20 74J10 PDFBibTeX XMLCite \textit{E. Montseny} and \textit{C. Casenave}, J. Vib. Control 21, No. 5, 1012--1028 (2015; Zbl 1358.93119) Full Text: DOI HAL
Ye, H.; Liu, Fawang; Anh, V. Compact difference scheme for distributed-order time-fractional diffusion-wave equation on bounded domains. (English) Zbl 1349.65353 J. Comput. Phys. 298, 652-660 (2015). MSC: 65M06 65M12 35R11 PDFBibTeX XMLCite \textit{H. Ye} et al., J. Comput. Phys. 298, 652--660 (2015; Zbl 1349.65353) Full Text: DOI Link
Li, Zhiyuan; Liu, Yikan; Yamamoto, Masahiro Initial-boundary value problems for multi-term time-fractional diffusion equations with positive constant coefficients. (English) Zbl 1338.35471 Appl. Math. Comput. 257, 381-397 (2015). MSC: 35R11 PDFBibTeX XMLCite \textit{Z. Li} et al., Appl. Math. Comput. 257, 381--397 (2015; Zbl 1338.35471) Full Text: DOI arXiv
Kolokoltsov, Vassili On fully mixed and multidimensional extensions of the Caputo and Riemann-Liouville derivatives, related Markov processes and fractional differential equations. (English) Zbl 1321.26013 Fract. Calc. Appl. Anal. 18, No. 4, 1039-1073 (2015). MSC: 26A33 34A08 35S15 60J50 60J75 PDFBibTeX XMLCite \textit{V. Kolokoltsov}, Fract. Calc. Appl. Anal. 18, No. 4, 1039--1073 (2015; Zbl 1321.26013) Full Text: DOI arXiv
Bazhlekova, Emilia Completely monotone functions and some classes of fractional evolution equations. (English) Zbl 1332.26011 Integral Transforms Spec. Funct. 26, No. 9, 737-752 (2015). Reviewer: James Adedayo Oguntuase (Abeokuta) MSC: 26A33 33E12 35R11 47D06 PDFBibTeX XMLCite \textit{E. Bazhlekova}, Integral Transforms Spec. Funct. 26, No. 9, 737--752 (2015; Zbl 1332.26011) Full Text: DOI arXiv
Caputo, Michele; Carcione, José M.; Botelho, Marco A. B. Modeling extreme-event precursors with the fractional diffusion equation. (English) Zbl 1515.35308 Fract. Calc. Appl. Anal. 18, No. 1, 208-222 (2015). MSC: 35R11 86A15 86-08 PDFBibTeX XMLCite \textit{M. Caputo} et al., Fract. Calc. Appl. Anal. 18, No. 1, 208--222 (2015; Zbl 1515.35308) Full Text: DOI
Morgado, M. L.; Rebelo, M. Numerical approximation of distributed order reaction-diffusion equations. (English) Zbl 1298.35242 J. Comput. Appl. Math. 275, 216-227 (2015). MSC: 35R11 35K57 65M06 65M12 PDFBibTeX XMLCite \textit{M. L. Morgado} and \textit{M. Rebelo}, J. Comput. Appl. Math. 275, 216--227 (2015; Zbl 1298.35242) Full Text: DOI
Li, Zhiyuan; Luchko, Yuri; Yamamoto, Masahiro Asymptotic estimates of solutions to initial-boundary-value problems for distributed order time-fractional diffusion equations. (English) Zbl 1312.35184 Fract. Calc. Appl. Anal. 17, No. 4, 1114-1136 (2014). MSC: 35R11 35B40 35S11 44A10 PDFBibTeX XMLCite \textit{Z. Li} et al., Fract. Calc. Appl. Anal. 17, No. 4, 1114--1136 (2014; Zbl 1312.35184) Full Text: DOI
Mijena, Jebessa B.; Nane, Erkan Strong analytic solutions of fractional Cauchy problems. (English) Zbl 1284.35457 Proc. Am. Math. Soc. 142, No. 5, 1717-1731 (2014). MSC: 35R11 35C15 35S05 47G30 60K99 PDFBibTeX XMLCite \textit{J. B. Mijena} and \textit{E. Nane}, Proc. Am. Math. Soc. 142, No. 5, 1717--1731 (2014; Zbl 1284.35457) Full Text: DOI arXiv
Jiao, Zhuang; Chen, YangQuan; Zhong, Yisheng Stability analysis of linear time-invariant distributed-order systems. (English) Zbl 1327.93340 Asian J. Control 15, No. 3, 640-647 (2013). MSC: 93D25 34A08 93C05 PDFBibTeX XMLCite \textit{Z. Jiao} et al., Asian J. Control 15, No. 3, 640--647 (2013; Zbl 1327.93340) Full Text: DOI arXiv
Gorenflo, Rudolf; Luchko, Yuri; Stojanović, Mirjana Fundamental solution of a distributed order time-fractional diffusion-wave equation as probability density. (English) Zbl 1312.35179 Fract. Calc. Appl. Anal. 16, No. 2, 297-316 (2013). MSC: 35R11 33E12 35S10 45K05 PDFBibTeX XMLCite \textit{R. Gorenflo} et al., Fract. Calc. Appl. Anal. 16, No. 2, 297--316 (2013; Zbl 1312.35179) Full Text: DOI
Jiang, H.; Liu, Fawang; Turner, I.; Burrage, K. Analytical solutions for the multi-term time-fractional diffusion-wave/diffusion equations in a finite domain. (English) Zbl 1268.35124 Comput. Math. Appl. 64, No. 10, 3377-3388 (2012). MSC: 35R11 35C10 PDFBibTeX XMLCite \textit{H. Jiang} et al., Comput. Math. Appl. 64, No. 10, 3377--3388 (2012; Zbl 1268.35124) Full Text: DOI
Luchko, Yury; Mainardi, Francesco; Rogosin, Sergei Professor Rudolf Gorenflo and his contribution to fractional calculus. (English) Zbl 1273.01048 Fract. Calc. Appl. Anal. 14, No. 1, 3-18 (2011). MSC: 01A70 01A60 26-03 26A33 PDFBibTeX XMLCite \textit{Y. Luchko} et al., Fract. Calc. Appl. Anal. 14, No. 1, 3--18 (2011; Zbl 1273.01048) Full Text: DOI Link
Caputo, Michele; Carcione, José M. Wave simulation in dissipative media described by distributed-order fractional time derivatives. (English) Zbl 1271.74233 J. Vib. Control 17, No. 8, 1121-1130 (2011). MSC: 74J10 26A33 PDFBibTeX XMLCite \textit{M. Caputo} and \textit{J. M. Carcione}, J. Vib. Control 17, No. 8, 1121--1130 (2011; Zbl 1271.74233) Full Text: DOI
Kochubei, Anatoly N. General fractional calculus, evolution equations, and renewal processes. (English) Zbl 1250.26006 Integral Equations Oper. Theory 71, No. 4, 583-600 (2011). Reviewer: Juan J. Trujillo (La Laguna) MSC: 26A33 34A08 60K05 PDFBibTeX XMLCite \textit{A. N. Kochubei}, Integral Equations Oper. Theory 71, No. 4, 583--600 (2011; Zbl 1250.26006) Full Text: DOI arXiv
Li, Yan; Sheng, Hu; Chen, Yang Quan On distributed order integrator/differentiator. (English) Zbl 1219.94039 Signal Process. 91, No. 5, 1079-1084 (2011). MSC: 94A12 26A33 65R20 PDFBibTeX XMLCite \textit{Y. Li} et al., Signal Process. 91, No. 5, 1079--1084 (2011; Zbl 1219.94039) Full Text: DOI
Veillette, Mark; Taqqu, Murad S. Numerical computation of first-passage times of increasing Lévy processes. (English) Zbl 1213.60094 Methodol. Comput. Appl. Probab. 12, No. 4, 695-729 (2010). Reviewer: Johannes Muhle-Karbe (Zürich) MSC: 60G51 60G40 60J75 60E07 PDFBibTeX XMLCite \textit{M. Veillette} and \textit{M. S. Taqqu}, Methodol. Comput. Appl. Probab. 12, No. 4, 695--729 (2010; Zbl 1213.60094) Full Text: DOI arXiv
Podlubny, Igor; Chechkin, Aleksei; Skovranek, Tomas; Chen, Yangquan; Vinagre Jara, Blas M. Matrix approach to discrete fractional calculus. II: Partial fractional differential equations. (English) Zbl 1160.65308 J. Comput. Phys. 228, No. 8, 3137-3153 (2009). MSC: 65D25 65M06 91B82 65Z05 PDFBibTeX XMLCite \textit{I. Podlubny} et al., J. Comput. Phys. 228, No. 8, 3137--3153 (2009; Zbl 1160.65308) Full Text: DOI arXiv
Shen, S.; Liu, Fawang; Anh, V. Fundamental solution and discrete random walk model for a time-space fractional diffusion equation of distributed order. (English) Zbl 1157.65520 J. Appl. Math. Comput. 28, No. 1-2, 147-164 (2008). MSC: 65R20 45K05 26A33 65M06 65G50 46F10 60H25 PDFBibTeX XMLCite \textit{S. Shen} et al., J. Appl. Math. Comput. 28, No. 1--2, 147--164 (2008; Zbl 1157.65520) Full Text: DOI Link