Hendy, Ahmed S.; Taha, T. R.; Suragan, D.; Zaky, Mahmoud A. An energy-preserving computational approach for the semilinear space fractional damped Klein-Gordon equation with a generalized scalar potential. (English) Zbl 1503.65229 Appl. Math. Modelling 108, 512-530 (2022). MSC: 65M60 35R11 PDFBibTeX XMLCite \textit{A. S. Hendy} et al., Appl. Math. Modelling 108, 512--530 (2022; Zbl 1503.65229) Full Text: DOI
Cao, Jiawei; Chen, Yiming; Wang, Yuanhui; Cheng, Gang; Barrière, Thierry; Wang, Lei Numerical analysis of fractional viscoelastic column based on shifted Chebyshev wavelet function. (English) Zbl 1481.74428 Appl. Math. Modelling 91, 374-389 (2021). MSC: 74K10 35R11 65M70 65T60 74D05 74S22 PDFBibTeX XMLCite \textit{J. Cao} et al., Appl. Math. Modelling 91, 374--389 (2021; Zbl 1481.74428) Full Text: DOI
Chen, Yuli; Liu, Fawang; Yu, Qiang; Li, Tianzeng Review of fractional epidemic models. (English) Zbl 1481.92135 Appl. Math. Modelling 97, 281-307 (2021). MSC: 92D30 26A33 34A08 34C60 PDFBibTeX XMLCite \textit{Y. Chen} et al., Appl. Math. Modelling 97, 281--307 (2021; Zbl 1481.92135) Full Text: DOI
Maurya, Rahul Kumar; Devi, Vinita; Singh, Vineet Kumar Stability and convergence of multistep schemes for 1D and 2D fractional model with nonlinear source term. (English) Zbl 1481.65149 Appl. Math. Modelling 89, Part 2, 1721-1746 (2021). MSC: 65M06 65M12 35R11 PDFBibTeX XMLCite \textit{R. K. Maurya} et al., Appl. Math. Modelling 89, Part 2, 1721--1746 (2021; Zbl 1481.65149) Full Text: DOI
Sweilam, N. H.; AL-Mekhlafi, S. M.; Albalawi, A. O.; Tenreiro Machado, J. A. Optimal control of variable-order fractional model for delay cancer treatments. (English) Zbl 1481.92071 Appl. Math. Modelling 89, Part 2, 1557-1574 (2021). MSC: 92C50 34A08 49N90 PDFBibTeX XMLCite \textit{N. H. Sweilam} et al., Appl. Math. Modelling 89, Part 2, 1557--1574 (2021; Zbl 1481.92071) Full Text: DOI
Gao, Yunfei; Yin, Deshun A full-stage creep model for rocks based on the variable-order fractional calculus. (English) Zbl 1481.74541 Appl. Math. Modelling 95, 435-446 (2021). MSC: 74L10 74S40 PDFBibTeX XMLCite \textit{Y. Gao} and \textit{D. Yin}, Appl. Math. Modelling 95, 435--446 (2021; Zbl 1481.74541) Full Text: DOI
Nikan, O.; Avazzadeh, Z.; Tenreiro Machado, J. A. Numerical approach for modeling fractional heat conduction in porous medium with the generalized Cattaneo model. (English) Zbl 1481.65150 Appl. Math. Modelling 100, 107-124 (2021). MSC: 65M06 35R11 65M12 80A19 PDFBibTeX XMLCite \textit{O. Nikan} et al., Appl. Math. Modelling 100, 107--124 (2021; Zbl 1481.65150) Full Text: DOI
Kuttler, Ch.; Maslovskaya, A. Hybrid stochastic fractional-based approach to modeling bacterial quorum sensing. (English) Zbl 1481.92084 Appl. Math. Modelling 93, 360-375 (2021). MSC: 92C70 35Q92 65M06 PDFBibTeX XMLCite \textit{Ch. Kuttler} and \textit{A. Maslovskaya}, Appl. Math. Modelling 93, 360--375 (2021; Zbl 1481.92084) Full Text: DOI
Nguyen, Du Dinh; Nguyen, Minh Ngoc; Duc, Nguyen Dinh; Rungamornrat, Jaroon; Bui, Tinh Quoc Enhanced nodal gradient finite elements with new numerical integration schemes for 2D and 3D geometrically nonlinear analysis. (English) Zbl 1481.65230 Appl. Math. Modelling 93, 326-359 (2021). MSC: 65N30 74S05 PDFBibTeX XMLCite \textit{D. D. Nguyen} et al., Appl. Math. Modelling 93, 326--359 (2021; Zbl 1481.65230) Full Text: DOI
Kumar, Abhishek; Rajeev A moving boundary problem with space-fractional diffusion logistic population model and density-dependent dispersal rate. (English) Zbl 1481.92104 Appl. Math. Modelling 88, 951-965 (2020). MSC: 92D25 35R11 PDFBibTeX XMLCite \textit{A. Kumar} and \textit{Rajeev}, Appl. Math. Modelling 88, 951--965 (2020; Zbl 1481.92104) Full Text: DOI
Lu, Bingqing; Liu, Xiaoting; Dong, Peiyao; Tick, Geoffrey R.; Zheng, Chunmiao; Zhang, Yong; Mahmood-UI-Hassan, Muhammad; Bai, Hongjuan; Lamy, Edvina Quantifying fate and transport of nitrate in saturated soil systems using fractional derivative model. (English) Zbl 1481.76217 Appl. Math. Modelling 81, 279-295 (2020). MSC: 76S05 35R11 PDFBibTeX XMLCite \textit{B. Lu} et al., Appl. Math. Modelling 81, 279--295 (2020; Zbl 1481.76217) Full Text: DOI
Zhang, Yanjie; Wang, Xiao; Huang, Qiao; Duan, Jinqiao; Li, Tingting Numerical analysis and applications of Fokker-Planck equations for stochastic dynamical systems with multiplicative \(\alpha \)-stable noises. (English) Zbl 1481.65027 Appl. Math. Modelling 87, 711-730 (2020). MSC: 65C30 60G52 60H10 PDFBibTeX XMLCite \textit{Y. Zhang} et al., Appl. Math. Modelling 87, 711--730 (2020; Zbl 1481.65027) Full Text: DOI arXiv
Cao Labora, Daniel; Lopes, António M.; Machado, J. A. Tenreiro Time-fractional dependence of the shear force in some beam type problems with negative Young modulus. (English) Zbl 1481.74429 Appl. Math. Modelling 80, 668-682 (2020). MSC: 74K10 PDFBibTeX XMLCite \textit{D. Cao Labora} et al., Appl. Math. Modelling 80, 668--682 (2020; Zbl 1481.74429) Full Text: DOI
Yang, Weidong; Chen, Xuehui; Zhang, Xinru; Zheng, Liancun; Liu, Fawang Flow and heat transfer of double fractional Maxwell fluids over a stretching sheet with variable thickness. (English) Zbl 1481.76281 Appl. Math. Modelling 80, 204-216 (2020). MSC: 76V05 35R11 PDFBibTeX XMLCite \textit{W. Yang} et al., Appl. Math. Modelling 80, 204--216 (2020; Zbl 1481.76281) Full Text: DOI
Gu, Yan; Sun, HongGuang A meshless method for solving three-dimensional time fractional diffusion equation with variable-order derivatives. (English) Zbl 1481.65130 Appl. Math. Modelling 78, 539-549 (2020). MSC: 65M06 35R11 PDFBibTeX XMLCite \textit{Y. Gu} and \textit{H. Sun}, Appl. Math. Modelling 78, 539--549 (2020; Zbl 1481.65130) Full Text: DOI
Li, Shu-Nan; Cao, Bing-Yang A superstatistical model for anomalous heat conduction and diffusion. (English) Zbl 1481.80005 Appl. Math. Modelling 79, 392-401 (2020). MSC: 80A19 PDFBibTeX XMLCite \textit{S.-N. Li} and \textit{B.-Y. Cao}, Appl. Math. Modelling 79, 392--401 (2020; Zbl 1481.80005) Full Text: DOI
Shi, Y. H.; Liu, F.; Zhao, Y. M.; Wang, F. L.; Turner, I. An unstructured mesh finite element method for solving the multi-term time fractional and Riesz space distributed-order wave equation on an irregular convex domain. (English) Zbl 1481.65190 Appl. Math. Modelling 73, 615-636 (2019). MSC: 65M60 35R11 65M12 PDFBibTeX XMLCite \textit{Y. H. Shi} et al., Appl. Math. Modelling 73, 615--636 (2019; Zbl 1481.65190) Full Text: DOI
Guo, Shimin; Mei, Liquan; Zhang, Zhengqiang; Chen, Jie; He, Yuan; Li, Ying Finite difference/Hermite-Galerkin spectral method for multi-dimensional time-fractional nonlinear reaction-diffusion equation in unbounded domains. (English) Zbl 1464.65141 Appl. Math. Modelling 70, 246-263 (2019). MSC: 65M70 65M06 65M12 35K57 35Q79 35R11 PDFBibTeX XMLCite \textit{S. Guo} et al., Appl. Math. Modelling 70, 246--263 (2019; Zbl 1464.65141) Full Text: DOI
Zhou, H. W.; Yang, S.; Zhang, S. Q. Modeling non-Darcian flow and solute transport in porous media with the Caputo-Fabrizio derivative. (English) Zbl 1481.76234 Appl. Math. Modelling 68, 603-615 (2019). MSC: 76S05 35R11 PDFBibTeX XMLCite \textit{H. W. Zhou} et al., Appl. Math. Modelling 68, 603--615 (2019; Zbl 1481.76234) Full Text: DOI
Chaudhary, Naveed Ishtiaq; Aslam khan, Zeshan; Zubair, Syed; Raja, Muhammad Asif Zahoor; Dedovic, Nebojsa Normalized fractional adaptive methods for nonlinear control autoregressive systems. (English) Zbl 1481.93147 Appl. Math. Modelling 66, 457-471 (2019). MSC: 93E35 PDFBibTeX XMLCite \textit{N. I. Chaudhary} et al., Appl. Math. Modelling 66, 457--471 (2019; Zbl 1481.93147) Full Text: DOI
Fan, Yu; Liu, Lin; Zheng, Liancun Anomalous subdiffusion in angular and radial direction on a circular comb-like structure with nonisotropic relaxation. (English) Zbl 1480.82007 Appl. Math. Modelling 64, 615-623 (2018). MSC: 82B05 80A19 PDFBibTeX XMLCite \textit{Y. Fan} et al., Appl. Math. Modelling 64, 615--623 (2018; Zbl 1480.82007) Full Text: DOI
Liu, Lin; Zheng, Liancun; Chen, Yanping Macroscopic and microscopic anomalous diffusion in comb model with fractional dual-phase-lag model. (English) Zbl 1460.82022 Appl. Math. Modelling 62, 629-637 (2018). MSC: 82C41 26A33 42A38 44A10 PDFBibTeX XMLCite \textit{L. Liu} et al., Appl. Math. Modelling 62, 629--637 (2018; Zbl 1460.82022) Full Text: DOI
Chen, Shanzhen; Liu, Fawang; Turner, Ian; Hu, Xiuling Numerical inversion of the fractional derivative index and surface thermal flux for an anomalous heat conduction model in a multi-layer medium. (English) Zbl 1480.35389 Appl. Math. Modelling 59, 514-526 (2018). MSC: 35R11 35R05 65M32 PDFBibTeX XMLCite \textit{S. Chen} et al., Appl. Math. Modelling 59, 514--526 (2018; Zbl 1480.35389) Full Text: DOI Link
Feng, Libo; Liu, Fawang; Turner, Ian; Yang, Qianqian; Zhuang, Pinghui Unstructured mesh finite difference/finite element method for the 2D time-space Riesz fractional diffusion equation on irregular convex domains. (English) Zbl 1480.65253 Appl. Math. Modelling 59, 441-463 (2018). MSC: 65M60 35R11 65M06 PDFBibTeX XMLCite \textit{L. Feng} et al., Appl. Math. Modelling 59, 441--463 (2018; Zbl 1480.65253) Full Text: DOI Link
Dabiri, Arman; Butcher, Eric A. Numerical solution of multi-order fractional differential equations with multiple delays via spectral collocation methods. (English) Zbl 1480.65158 Appl. Math. Modelling 56, 424-448 (2018). MSC: 65L03 34K37 65L60 PDFBibTeX XMLCite \textit{A. Dabiri} and \textit{E. A. Butcher}, Appl. Math. Modelling 56, 424--448 (2018; Zbl 1480.65158) Full Text: DOI
Pan, Mingyang; Zheng, Liancun; Liu, Fawang; Liu, Chunyan; Chen, Xuehui A spatial-fractional thermal transport model for nanofluid in porous media. (English) Zbl 1480.76123 Appl. Math. Modelling 53, 622-634 (2018). MSC: 76S05 PDFBibTeX XMLCite \textit{M. Pan} et al., Appl. Math. Modelling 53, 622--634 (2018; Zbl 1480.76123) Full Text: DOI Link
Sin, Chung-Sik; Zheng, Liancun; Sin, Jun-Sik; Liu, Fawang; Liu, Lin Unsteady flow of viscoelastic fluid with the fractional K-BKZ model between two parallel plates. (English) Zbl 1446.76043 Appl. Math. Modelling 47, 114-127 (2017). MSC: 76-10 PDFBibTeX XMLCite \textit{C.-S. Sin} et al., Appl. Math. Modelling 47, 114--127 (2017; Zbl 1446.76043) Full Text: DOI Link
Espinosa-Paredes, Gilberto; Cázares-Ramírez, Ricardo-I.; François, Juan-Luis; Martin-del-Campo, Cecilia On the stability of fractional neutron point kinetics (FNPK). (English) Zbl 1446.82001 Appl. Math. Modelling 45, 505-515 (2017). MSC: 82-10 34A08 82D75 PDFBibTeX XMLCite \textit{G. Espinosa-Paredes} et al., Appl. Math. Modelling 45, 505--515 (2017; Zbl 1446.82001) Full Text: DOI
Reutskiy, S. Yu. A new semi-analytical collocation method for solving multi-term fractional partial differential equations with time variable coefficients. (English) Zbl 1446.65132 Appl. Math. Modelling 45, 238-254 (2017). MSC: 65M70 35R11 65M06 PDFBibTeX XMLCite \textit{S. Yu. Reutskiy}, Appl. Math. Modelling 45, 238--254 (2017; Zbl 1446.65132) Full Text: DOI
Oskouie, M. Faraji; Ansari, R. Linear and nonlinear vibrations of fractional viscoelastic Timoshenko nanobeams considering surface energy effects. (English) Zbl 1446.74041 Appl. Math. Modelling 43, 337-350 (2017). MSC: 74-10 74D05 74K10 74H45 PDFBibTeX XMLCite \textit{M. F. Oskouie} and \textit{R. Ansari}, Appl. Math. Modelling 43, 337--350 (2017; Zbl 1446.74041) Full Text: DOI
Zhao, Jinhu; Zheng, Liancun; Chen, Xuehui; Zhang, Xinxin; Liu, Fawang Unsteady Marangoni convection heat transfer of fractional Maxwell fluid with Cattaneo heat flux. (English) Zbl 1443.76094 Appl. Math. Modelling 44, 497-507 (2017). MSC: 76-10 76A05 PDFBibTeX XMLCite \textit{J. Zhao} et al., Appl. Math. Modelling 44, 497--507 (2017; Zbl 1443.76094) Full Text: DOI Link
Cusimano, Nicole; Burrage, Kevin; Turner, I.; Kay, David On reflecting boundary conditions for space-fractional equations on a finite interval: proof of the matrix transfer technique. (English) Zbl 1443.35166 Appl. Math. Modelling 42, 554-565 (2017). MSC: 35R11 PDFBibTeX XMLCite \textit{N. Cusimano} et al., Appl. Math. Modelling 42, 554--565 (2017; Zbl 1443.35166) Full Text: DOI
Li, J.; Liu, F.; Feng, L.; Turner, I. A novel finite volume method for the Riesz space distributed-order advection-diffusion equation. (English) Zbl 1443.65162 Appl. Math. Modelling 46, 536-553 (2017). MSC: 65M08 35R11 65M12 PDFBibTeX XMLCite \textit{J. Li} et al., Appl. Math. Modelling 46, 536--553 (2017; Zbl 1443.65162) Full Text: DOI
Zhao, Y. M.; Zhang, Y. D.; Liu, F.; Turner, I.; Shi, D. Y. Analytical solution and nonconforming finite element approximation for the 2D multi-term fractional subdiffusion equation. (English) Zbl 1471.65156 Appl. Math. Modelling 40, No. 19-20, 8810-8825 (2016). MSC: 65M60 65M12 35R11 PDFBibTeX XMLCite \textit{Y. M. Zhao} et al., Appl. Math. Modelling 40, No. 19--20, 8810--8825 (2016; Zbl 1471.65156) Full Text: DOI
Nguyen, Huy Tuan; Le, Dinh Long; Nguyen, Van Thinh Regularized solution of an inverse source problem for a time fractional diffusion equation. (English) Zbl 1471.65124 Appl. Math. Modelling 40, No. 19-20, 8244-8264 (2016). MSC: 65M32 35R11 PDFBibTeX XMLCite \textit{H. T. Nguyen} et al., Appl. Math. Modelling 40, No. 19--20, 8244--8264 (2016; Zbl 1471.65124) Full Text: DOI
Wei, Ting; Wang, Jun-Gang Determination of Robin coefficient in a fractional diffusion problem. (English) Zbl 1471.65127 Appl. Math. Modelling 40, No. 17-18, 7948-7961 (2016). MSC: 65M32 35R11 PDFBibTeX XMLCite \textit{T. Wei} and \textit{J.-G. Wang}, Appl. Math. Modelling 40, No. 17--18, 7948--7961 (2016; Zbl 1471.65127) Full Text: DOI
Yuan, Z. B.; Nie, Y. F.; Liu, F.; Turner, I.; Zhang, G. Y.; Gu, Y. T. An advanced numerical modeling for Riesz space fractional advection-dispersion equations by a meshfree approach. (English) Zbl 1471.65167 Appl. Math. Modelling 40, No. 17-18, 7816-7829 (2016). MSC: 65M70 35R11 PDFBibTeX XMLCite \textit{Z. B. Yuan} et al., Appl. Math. Modelling 40, No. 17--18, 7816--7829 (2016; Zbl 1471.65167) Full Text: DOI
Carr, Elliot J.; Turner, I. W. A semi-analytical solution for multilayer diffusion in a composite medium consisting of a large number of layers. (English) Zbl 1471.74014 Appl. Math. Modelling 40, No. 15-16, 7034-7050 (2016). MSC: 74E30 74H05 74H10 74H15 PDFBibTeX XMLCite \textit{E. J. Carr} and \textit{I. W. Turner}, Appl. Math. Modelling 40, No. 15--16, 7034--7050 (2016; Zbl 1471.74014) Full Text: DOI
Tatar, Salih; Tınaztepe, Ramazan; Muradoğlu, Zahir Simultaneous determination of the strain hardening exponent, the shear modulus and the elastic stress limit in an inverse problem. (English) Zbl 1471.74021 Appl. Math. Modelling 40, No. 15-16, 6956-6968 (2016). MSC: 74G70 74A10 PDFBibTeX XMLCite \textit{S. Tatar} et al., Appl. Math. Modelling 40, No. 15--16, 6956--6968 (2016; Zbl 1471.74021) Full Text: DOI
Liu, Lin; Zheng, Liancun; Zhang, Xinxin Fractional anomalous diffusion with Cattaneo-Christov flux effects in a comb-like structure. (English) Zbl 1465.82009 Appl. Math. Modelling 40, No. 13-14, 6663-6675 (2016). MSC: 82C70 PDFBibTeX XMLCite \textit{L. Liu} et al., Appl. Math. Modelling 40, No. 13--14, 6663--6675 (2016; Zbl 1465.82009) Full Text: DOI
Li, Dongfang; Zhang, Chengjian; Ran, Maohua A linear finite difference scheme for generalized time fractional Burgers equation. (English) Zbl 1465.65075 Appl. Math. Modelling 40, No. 11-12, 6069-6081 (2016). MSC: 65M06 35Q53 35R11 PDFBibTeX XMLCite \textit{D. Li} et al., Appl. Math. Modelling 40, No. 11--12, 6069--6081 (2016; Zbl 1465.65075) Full Text: DOI
Zhang, H.; Liu, F.; Turner, I.; Chen, S. The numerical simulation of the tempered fractional Black-Scholes equation for European double barrier option. (English) Zbl 1465.91131 Appl. Math. Modelling 40, No. 11-12, 5819-5834 (2016). MSC: 91G60 65M06 65M12 91G20 PDFBibTeX XMLCite \textit{H. Zhang} et al., Appl. Math. Modelling 40, No. 11--12, 5819--5834 (2016; Zbl 1465.91131) Full Text: DOI
Zheng, M.; Liu, F.; Anh, V.; Turner, I. A high-order spectral method for the multi-term time-fractional diffusion equations. (English) Zbl 1459.65205 Appl. Math. Modelling 40, No. 7-8, 4970-4985 (2016). MSC: 65M70 65M12 35R11 PDFBibTeX XMLCite \textit{M. Zheng} et al., Appl. Math. Modelling 40, No. 7--8, 4970--4985 (2016; Zbl 1459.65205) Full Text: DOI
Si, Xinhui; Wang, Chao; Shen, Yanan; Zheng, Liancun Numerical method to initial-boundary value problems for fractional partial differential equations with time-space variable coefficients. (English) Zbl 1459.65202 Appl. Math. Modelling 40, No. 7-8, 4397-4411 (2016). MSC: 65M70 65M15 65T60 35R11 PDFBibTeX XMLCite \textit{X. Si} et al., Appl. Math. Modelling 40, No. 7--8, 4397--4411 (2016; Zbl 1459.65202) Full Text: DOI
Dehghan, Mehdi; Abbaszadeh, Mostafa; Mohebbi, Akbar Legendre spectral element method for solving time fractional modified anomalous sub-diffusion equation. (English) Zbl 1459.65194 Appl. Math. Modelling 40, No. 5-6, 3635-3654 (2016). MSC: 65M70 35R11 PDFBibTeX XMLCite \textit{M. Dehghan} et al., Appl. Math. Modelling 40, No. 5--6, 3635--3654 (2016; Zbl 1459.65194) Full Text: DOI
Mollahasani, N.; Moghadam, M. Mohseni; Afrooz, K. A new treatment based on hybrid functions to the solution of telegraph equations of fractional order. (English) Zbl 1452.35243 Appl. Math. Modelling 40, No. 4, 2804-2814 (2016). MSC: 35R11 PDFBibTeX XMLCite \textit{N. Mollahasani} et al., Appl. Math. Modelling 40, No. 4, 2804--2814 (2016; Zbl 1452.35243) Full Text: DOI
Ren, Jincheng; Sun, Zhi-zhong; Dai, Weizhong New approximations for solving the Caputo-type fractional partial differential equations. (English) Zbl 1452.65176 Appl. Math. Modelling 40, No. 4, 2625-2636 (2016). MSC: 65M06 35R11 PDFBibTeX XMLCite \textit{J. Ren} et al., Appl. Math. Modelling 40, No. 4, 2625--2636 (2016; Zbl 1452.65176) Full Text: DOI
Hu, Xiuling; Zhang, Luming An analysis of a second order difference scheme for the fractional subdiffusion system. (English) Zbl 1446.65067 Appl. Math. Modelling 40, No. 2, 1634-1649 (2016). MSC: 65M06 35R11 65M12 PDFBibTeX XMLCite \textit{X. Hu} and \textit{L. Zhang}, Appl. Math. Modelling 40, No. 2, 1634--1649 (2016; Zbl 1446.65067) Full Text: DOI
Zhai, Shuying; Weng, Zhifeng; Feng, Xinlong Fast explicit operator splitting method and time-step adaptivity for fractional non-local Allen-Cahn model. (English) Zbl 1446.65135 Appl. Math. Modelling 40, No. 2, 1315-1324 (2016). MSC: 65M70 35R11 35K57 PDFBibTeX XMLCite \textit{S. Zhai} et al., Appl. Math. Modelling 40, No. 2, 1315--1324 (2016; Zbl 1446.65135) Full Text: DOI
Bhrawy, A. H.; Zaky, M. A. Shifted fractional-order Jacobi orthogonal functions: application to a system of fractional differential equations. (English) Zbl 1446.34011 Appl. Math. Modelling 40, No. 2, 832-845 (2016). MSC: 34A08 26A33 33C47 65L60 PDFBibTeX XMLCite \textit{A. H. Bhrawy} and \textit{M. A. Zaky}, Appl. Math. Modelling 40, No. 2, 832--845 (2016; Zbl 1446.34011) Full Text: DOI
Khosravian-Arab, Hassan; Almeida, Ricardo Numerical solution for fractional variational problems using the Jacobi polynomials. (English) Zbl 1443.49039 Appl. Math. Modelling 39, No. 21, 6461-6470 (2015). MSC: 49M99 26A33 49K21 PDFBibTeX XMLCite \textit{H. Khosravian-Arab} and \textit{R. Almeida}, Appl. Math. Modelling 39, No. 21, 6461--6470 (2015; Zbl 1443.49039) Full Text: DOI arXiv
Wang, Jun-Gang; Wei, Ting Quasi-reversibility method to identify a space-dependent source for the time-fractional diffusion equation. (English) Zbl 1443.35198 Appl. Math. Modelling 39, No. 20, 6139-6149 (2015). MSC: 35R30 35R11 PDFBibTeX XMLCite \textit{J.-G. Wang} and \textit{T. Wei}, Appl. Math. Modelling 39, No. 20, 6139--6149 (2015; Zbl 1443.35198) Full Text: DOI
Nazari Susahab, D.; Shahmorad, S.; Jahanshahi, M. Efficient quadrature rules for solving nonlinear fractional integro-differential equations of the Hammerstein type. (English) Zbl 1443.65444 Appl. Math. Modelling 39, No. 18, 5452-5458 (2015). MSC: 65R20 45G10 PDFBibTeX XMLCite \textit{D. Nazari Susahab} et al., Appl. Math. Modelling 39, No. 18, 5452--5458 (2015; Zbl 1443.65444) Full Text: DOI
Gupta, A. K.; Saha Ray, S. Numerical treatment for the solution of fractional fifth-order Sawada-Kotera equation using second kind Chebyshev wavelet method. (English) Zbl 1443.65244 Appl. Math. Modelling 39, No. 17, 5121-5130 (2015). MSC: 65M70 35R11 PDFBibTeX XMLCite \textit{A. K. Gupta} and \textit{S. Saha Ray}, Appl. Math. Modelling 39, No. 17, 5121--5130 (2015; Zbl 1443.65244) Full Text: DOI
Maleki Moghaddam, Nader; Afarideh, Hossein; Espinosa-Paredes, Gilberto Development of a 2D-multigroup code (NFDE-2D) based on the neutron spatial-fractional diffusion equation. (English) Zbl 1443.65133 Appl. Math. Modelling 39, No. 13, 3637-3652 (2015). MSC: 65M06 35R11 82D75 PDFBibTeX XMLCite \textit{N. Maleki Moghaddam} et al., Appl. Math. Modelling 39, No. 13, 3637--3652 (2015; Zbl 1443.65133) Full Text: DOI
Gao, Xiaolong; Jiang, Xiaoyun; Chen, Shanzhen The numerical method for the moving boundary problem with space-fractional derivative in drug release devices. (English) Zbl 1443.92099 Appl. Math. Modelling 39, No. 8, 2385-2391 (2015). MSC: 92C50 35R11 92-08 PDFBibTeX XMLCite \textit{X. Gao} et al., Appl. Math. Modelling 39, No. 8, 2385--2391 (2015; Zbl 1443.92099) Full Text: DOI
Yang, J. Y.; Zhao, Y. M.; Liu, N.; Bu, W. P.; Xu, T. L.; Tang, Y. F. An implicit MLS meshless method for 2-D time dependent fractional diffusion-wave equation. (English) Zbl 1432.65129 Appl. Math. Modelling 39, No. 3-4, 1229-1240 (2015). MSC: 65M06 35R11 45K05 65M12 76M20 PDFBibTeX XMLCite \textit{J. Y. Yang} et al., Appl. Math. Modelling 39, No. 3--4, 1229--1240 (2015; Zbl 1432.65129) Full Text: DOI
Jiang, Yingjun A new analysis of stability and convergence for finite difference schemes solving the time fractional Fokker-Planck equation. (English) Zbl 1432.65122 Appl. Math. Modelling 39, No. 3-4, 1163-1171 (2015). MSC: 65M06 35R11 65M12 PDFBibTeX XMLCite \textit{Y. Jiang}, Appl. Math. Modelling 39, No. 3--4, 1163--1171 (2015; Zbl 1432.65122) Full Text: DOI
Liu, F.; Zhuang, P.; Turner, I.; Burrage, K.; Anh, V. A new fractional finite volume method for solving the fractional diffusion equation. (English) Zbl 1429.65213 Appl. Math. Modelling 38, No. 15-16, 3871-3878 (2014). MSC: 65M08 35R11 PDFBibTeX XMLCite \textit{F. Liu} et al., Appl. Math. Modelling 38, No. 15--16, 3871--3878 (2014; Zbl 1429.65213) Full Text: DOI
Zhuang, P.; Liu, F.; Turner, I.; Gu, Y. T. Finite volume and finite element methods for solving a one-dimensional space-fractional Boussinesq equation. (English) Zbl 1429.65233 Appl. Math. Modelling 38, No. 15-16, 3860-3870 (2014). MSC: 65M60 35R11 65M08 PDFBibTeX XMLCite \textit{P. Zhuang} et al., Appl. Math. Modelling 38, No. 15--16, 3860--3870 (2014; Zbl 1429.65233) Full Text: DOI
Zhao, Xuan; Xu, Qinwu Efficient numerical schemes for fractional sub-diffusion equation with the spatially variable coefficient. (English) Zbl 1429.65210 Appl. Math. Modelling 38, No. 15-16, 3848-3859 (2014). MSC: 65M06 35R11 65M12 PDFBibTeX XMLCite \textit{X. Zhao} and \textit{Q. Xu}, Appl. Math. Modelling 38, No. 15--16, 3848--3859 (2014; Zbl 1429.65210) Full Text: DOI
Li, Changpin; Ding, Hengfei Higher order finite difference method for the reaction and anomalous-diffusion equation. (English) Zbl 1429.65188 Appl. Math. Modelling 38, No. 15-16, 3802-3821 (2014). MSC: 65M06 35R11 65M12 PDFBibTeX XMLCite \textit{C. Li} and \textit{H. Ding}, Appl. Math. Modelling 38, No. 15--16, 3802--3821 (2014; Zbl 1429.65188) Full Text: DOI
Yang, Qianqian; Turner, Ian; Moroney, Timothy; Liu, Fawang A finite volume scheme with preconditioned Lanczos method for two-dimensional space-fractional reaction-diffusion equations. (English) Zbl 1429.65215 Appl. Math. Modelling 38, No. 15-16, 3755-3762 (2014). MSC: 65M08 35R11 65F10 PDFBibTeX XMLCite \textit{Q. Yang} et al., Appl. Math. Modelling 38, No. 15--16, 3755--3762 (2014; Zbl 1429.65215) Full Text: DOI
Chen, J.; Liu, F.; Liu, Q.; Chen, X.; Anh, V.; Turner, I.; Burrage, K. Numerical simulation for the three-dimension fractional sub-diffusion equation. (English) Zbl 1429.65179 Appl. Math. Modelling 38, No. 15-16, 3695-3705 (2014). MSC: 65M06 35R11 65M12 PDFBibTeX XMLCite \textit{J. Chen} et al., Appl. Math. Modelling 38, No. 15--16, 3695--3705 (2014; Zbl 1429.65179) Full Text: DOI
Yang, J. Y.; Huang, J. F.; Liang, D. M.; Tang, Y. F. Numerical solution of fractional diffusion-wave equation based on fractional multistep method. (English) Zbl 1427.65196 Appl. Math. Modelling 38, No. 14, 3652-3661 (2014). MSC: 65M06 35R11 65M12 65R20 PDFBibTeX XMLCite \textit{J. Y. Yang} et al., Appl. Math. Modelling 38, No. 14, 3652--3661 (2014; Zbl 1427.65196) Full Text: DOI
Chen, Minghua; Deng, Weihua A second-order numerical method for two-dimensional two-sided space fractional convection diffusion equation. (English) Zbl 1427.65149 Appl. Math. Modelling 38, No. 13, 3244-3259 (2014). MSC: 65M06 35R11 65M12 76M20 PDFBibTeX XMLCite \textit{M. Chen} and \textit{W. Deng}, Appl. Math. Modelling 38, No. 13, 3244--3259 (2014; Zbl 1427.65149) Full Text: DOI arXiv
Kumar, Sunil A new analytical modelling for fractional telegraph equation via Laplace transform. (English) Zbl 1427.35327 Appl. Math. Modelling 38, No. 13, 3154-3163 (2014). MSC: 35R11 65M99 PDFBibTeX XMLCite \textit{S. Kumar}, Appl. Math. Modelling 38, No. 13, 3154--3163 (2014; Zbl 1427.35327) Full Text: DOI
Wei, Leilei; He, Yinnian Analysis of a fully discrete local discontinuous Galerkin method for time-fractional fourth-order problems. (English) Zbl 1427.65267 Appl. Math. Modelling 38, No. 4, 1511-1522 (2014). MSC: 65M60 35R11 65M06 65M12 65M15 PDFBibTeX XMLCite \textit{L. Wei} and \textit{Y. He}, Appl. Math. Modelling 38, No. 4, 1511--1522 (2014; Zbl 1427.65267) Full Text: DOI
Mai-Duy, N.; Thai-Quang, N.; Hoang-Trieu, T.-T.; Tran-Cong, T. A compact 9 point stencil based on integrated RBFs for the convection-diffusion equation. (English) Zbl 1427.65330 Appl. Math. Modelling 38, No. 4, 1495-1510 (2014). MSC: 65N06 65D12 76M99 PDFBibTeX XMLCite \textit{N. Mai-Duy} et al., Appl. Math. Modelling 38, No. 4, 1495--1510 (2014; Zbl 1427.65330) Full Text: DOI
Ma, Xiaohua; Huang, Chengming Spectral collocation method for linear fractional integro-differential equations. (English) Zbl 1427.65421 Appl. Math. Modelling 38, No. 4, 1434-1448 (2014). MSC: 65R20 34K37 45J05 65L60 PDFBibTeX XMLCite \textit{X. Ma} and \textit{C. Huang}, Appl. Math. Modelling 38, No. 4, 1434--1448 (2014; Zbl 1427.65421) Full Text: DOI
Wang, Jun-Gang; Wei, Ting; Zhou, Yu-Bin Tikhonov regularization method for a backward problem for the time-fractional diffusion equation. (English) Zbl 1427.65229 Appl. Math. Modelling 37, No. 18-19, 8518-8532 (2013). MSC: 65M32 35R11 35R30 PDFBibTeX XMLCite \textit{J.-G. Wang} et al., Appl. Math. Modelling 37, No. 18--19, 8518--8532 (2013; Zbl 1427.65229) Full Text: DOI
Atabakzadeh, M. H.; Akrami, M. H.; Erjaee, G. H. Chebyshev operational matrix method for solving multi-order fractional ordinary differential equations. (English) Zbl 1449.34010 Appl. Math. Modelling 37, No. 20-21, 8903-8911 (2013). MSC: 34A08 34A30 34A25 65L05 PDFBibTeX XMLCite \textit{M. H. Atabakzadeh} et al., Appl. Math. Modelling 37, No. 20--21, 8903--8911 (2013; Zbl 1449.34010) Full Text: DOI
Wu, Guo-Cheng; Baleanu, Dumitru Variational iteration method for the Burgers’ flow with fractional derivatives – new Lagrange multipliers. (English) Zbl 1438.76046 Appl. Math. Modelling 37, No. 9, 6183-6190 (2013). MSC: 76S05 26A33 65R20 65L05 44A10 45J05 35R11 76M30 PDFBibTeX XMLCite \textit{G.-C. Wu} and \textit{D. Baleanu}, Appl. Math. Modelling 37, No. 9, 6183--6190 (2013; Zbl 1438.76046) Full Text: DOI
Kazem, S.; Abbasbandy, S.; Kumar, Sunil Fractional-order Legendre functions for solving fractional-order differential equations. (English) Zbl 1449.33012 Appl. Math. Modelling 37, No. 7, 5498-5510 (2013). MSC: 33C45 26A33 34A08 65L60 PDFBibTeX XMLCite \textit{S. Kazem} et al., Appl. Math. Modelling 37, No. 7, 5498--5510 (2013; Zbl 1449.33012) Full Text: DOI
Kazem, Saeed An integral operational matrix based on Jacobi polynomials for solving fractional-order differential equations. (English) Zbl 1351.34007 Appl. Math. Modelling 37, No. 3, 1126-1136 (2013). MSC: 34A08 41A55 65L60 34A45 PDFBibTeX XMLCite \textit{S. Kazem}, Appl. Math. Modelling 37, No. 3, 1126--1136 (2013; Zbl 1351.34007) Full Text: DOI
Cheng, Hao; Fu, Chu-Li An iteration regularization for a time-fractional inverse diffusion problem. (English) Zbl 1254.65100 Appl. Math. Modelling 36, No. 11, 5642-5649 (2012). MSC: 65M32 35R11 PDFBibTeX XMLCite \textit{H. Cheng} and \textit{C.-L. Fu}, Appl. Math. Modelling 36, No. 11, 5642--5649 (2012; Zbl 1254.65100) Full Text: DOI
Hu, Xiuling; Zhang, Luming Implicit compact difference schemes for the fractional cable equation. (English) Zbl 1252.74061 Appl. Math. Modelling 36, No. 9, 4027-4043 (2012). MSC: 74S20 65M06 35R11 74K10 PDFBibTeX XMLCite \textit{X. Hu} and \textit{L. Zhang}, Appl. Math. Modelling 36, No. 9, 4027--4043 (2012; Zbl 1252.74061) Full Text: DOI
Liu, Q.; Liu, Fawang; Turner, I.; Anh, V. Finite element approximation for a modified anomalous subdiffusion equation. (English) Zbl 1221.65257 Appl. Math. Modelling 35, No. 8, 4103-4116 (2011). MSC: 65M60 35K20 35R11 65M12 PDFBibTeX XMLCite \textit{Q. Liu} et al., Appl. Math. Modelling 35, No. 8, 4103--4116 (2011; Zbl 1221.65257) Full Text: DOI
Guo, Zhongjin; Leung, A. Y. T.; Yang, H. X. Oscillatory region and asymptotic solution of fractional van der Pol oscillator via residue harmonic balance technique. (English) Zbl 1221.34011 Appl. Math. Modelling 35, No. 8, 3918-3925 (2011). MSC: 34A08 26A33 34C15 34E10 PDFBibTeX XMLCite \textit{Z. Guo} et al., Appl. Math. Modelling 35, No. 8, 3918--3925 (2011; Zbl 1221.34011) Full Text: DOI
Du, R.; Cao, W. R.; Sun, Z. Z. A compact difference scheme for the fractional diffusion-wave equation. (English) Zbl 1201.65154 Appl. Math. Modelling 34, No. 10, 2998-3007 (2010). MSC: 65M06 34A08 26A33 45K05 PDFBibTeX XMLCite \textit{R. Du} et al., Appl. Math. Modelling 34, No. 10, 2998--3007 (2010; Zbl 1201.65154) Full Text: DOI
Yang, Q.; Liu, Fawang; Turner, I. Numerical methods for fractional partial differential equations with Riesz space fractional derivatives. (English) Zbl 1185.65200 Appl. Math. Modelling 34, No. 1, 200-218 (2010). MSC: 65M99 26A33 35R11 PDFBibTeX XMLCite \textit{Q. Yang} et al., Appl. Math. Modelling 34, No. 1, 200--218 (2010; Zbl 1185.65200) Full Text: DOI
Chen, S.; Liu, Fawang; Zhuang, P.; Anh, V. Finite difference approximations for the fractional Fokker-Planck equation. (English) Zbl 1167.65419 Appl. Math. Modelling 33, No. 1, 256-273 (2009). MSC: 65M06 26A33 35K55 PDFBibTeX XMLCite \textit{S. Chen} et al., Appl. Math. Modelling 33, No. 1, 256--273 (2009; Zbl 1167.65419) Full Text: DOI
Odibat, Zaid; Momani, Shaher Numerical methods for nonlinear partial differential equations of fractional order. (English) Zbl 1133.65116 Appl. Math. Modelling 32, No. 1, 28-39 (2008). MSC: 65R20 45K05 65M70 35K55 26A33 PDFBibTeX XMLCite \textit{Z. Odibat} and \textit{S. Momani}, Appl. Math. Modelling 32, No. 1, 28--39 (2008; Zbl 1133.65116) Full Text: DOI Link
Liu, Fawang; Anh, V. V.; Turner, I.; Bajracharya, K.; Huxley, W. J.; Su, N. A finite volume simulation model for saturated–unsaturated flow and application to Gooburrum, Bundaberg, Queensland, Australia. (English) Zbl 1163.76392 Appl. Math. Modelling 30, No. 4, 352-366 (2006). MSC: 76M12 PDFBibTeX XMLCite \textit{F. Liu} et al., Appl. Math. Modelling 30, No. 4, 352--366 (2006; Zbl 1163.76392) Full Text: DOI
Zhao, H.; Turner, I. W. The use of a coupled computational model for studying the microwave heating of wood. (English) Zbl 0963.80010 Appl. Math. Modelling 24, No. 3, 183-197 (2000). MSC: 80M25 80A99 78M25 PDFBibTeX XMLCite \textit{H. Zhao} and \textit{I. W. Turner}, Appl. Math. Modelling 24, No. 3, 183--197 (2000; Zbl 0963.80010) Full Text: DOI