Jafari, Hossein; Prasad, Jyoti Geetesh; Goswami, Pranay; Dubey, Ravi Shanker Solution of the local fractional generalized KdV equation using homotopy analysis method. (English) Zbl 1482.35064 Fractals 29, No. 5, Article ID 2140014, 10 p. (2021). MSC: 35C05 35Q53 35R11 PDF BibTeX XML Cite \textit{H. Jafari} et al., Fractals 29, No. 5, Article ID 2140014, 10 p. (2021; Zbl 1482.35064) Full Text: DOI OpenURL
Oliveira, D. S.; de Oliveira, E. Capelas Analytical solutions for Navier-Stokes equations with Caputo fractional derivative. (English) Zbl 07443642 S\(\vec{\text{e}}\)MA J. 78, No. 1, 137-154 (2021). MSC: 35Q30 76D05 26A33 35G10 35R11 PDF BibTeX XML Cite \textit{D. S. Oliveira} and \textit{E. C. de Oliveira}, S\(\vec{\text{e}}\)MA J. 78, No. 1, 137--154 (2021; Zbl 07443642) Full Text: DOI arXiv OpenURL
Hajira, Hajira; Khan, Hassan; Khan, Adnan; Kumam, Poom; Baleanu, Dumitru; Arif, Muhammad An approximate analytical solution of the Navier-Stokes equations within Caputo operator and Elzaki transform decomposition method. (English) Zbl 07535347 Adv. Difference Equ. 2020, Paper No. 622, 22 p. (2020). MSC: 35R11 65R20 65M70 45K05 26A33 PDF BibTeX XML Cite \textit{H. Hajira} et al., Adv. Difference Equ. 2020, Paper No. 622, 22 p. (2020; Zbl 07535347) Full Text: DOI OpenURL
Zhang, Kangqun Existence of solution of space-time fractional diffusion-wave equation in weighted Sobolev space. (English) Zbl 1439.35551 Adv. Math. Phys. 2020, Article ID 1545043, 6 p. (2020). MSC: 35R11 PDF BibTeX XML Cite \textit{K. Zhang}, Adv. Math. Phys. 2020, Article ID 1545043, 6 p. (2020; Zbl 1439.35551) Full Text: DOI OpenURL
Mokhtar, Mahmoud M.; Mohamed, Amany S. Lucas polynomials semi-analytic solution for fractional multi-term initial value problems. (English) Zbl 07532444 Adv. Difference Equ. 2019, Paper No. 471, 13 p. (2019). MSC: 34A08 26A33 PDF BibTeX XML Cite \textit{M. M. Mokhtar} and \textit{A. S. Mohamed}, Adv. Difference Equ. 2019, Paper No. 471, 13 p. (2019; Zbl 07532444) Full Text: DOI OpenURL
Morales-Delgado, V. F.; Gómez-Aguilar, J. F.; Torres, L.; Escobar-Jiménez, R. F.; Taneco-Hernandez, M. A. Exact solutions for the Liénard type model via fractional homotopy methods. (English) Zbl 1437.35694 Gómez, José Francisco (ed.) et al., Fractional derivatives with Mittag-Leffler kernel. Trends and applications in science and engineering. Cham: Springer. Stud. Syst. Decis. Control 194, 269-291 (2019). MSC: 35R11 26A33 65M99 PDF BibTeX XML Cite \textit{V. F. Morales-Delgado} et al., Stud. Syst. Decis. Control 194, 269--291 (2019; Zbl 1437.35694) Full Text: DOI OpenURL
Kumar, Rakesh; Koundal, Reena; Shehzad, Sabir Ali Generalized least square homotopy perturbation solution of fractional telegraph equations. (English) Zbl 1438.65267 Comput. Appl. Math. 38, No. 4, Paper No. 184, 20 p. (2019). MSC: 65M99 35R11 PDF BibTeX XML Cite \textit{R. Kumar} et al., Comput. Appl. Math. 38, No. 4, Paper No. 184, 20 p. (2019; Zbl 1438.65267) Full Text: DOI OpenURL
Shamseldeen, S.; Elsaid, A.; Madkour, S. Caputo-Riesz-Feller fractional wave equation: analytic and approximate solutions and their continuation. (English) Zbl 1418.35366 J. Appl. Math. Comput. 59, No. 1-2, 423-444 (2019). MSC: 35R11 35C20 PDF BibTeX XML Cite \textit{S. Shamseldeen} et al., J. Appl. Math. Comput. 59, No. 1--2, 423--444 (2019; Zbl 1418.35366) Full Text: DOI OpenURL
Chohan, Muhammad Ikhlaq; Shah, Kamal On a computational method for non-integer order partial differential equations in two dimensions. (English) Zbl 1424.65182 Eur. J. Pure Appl. Math. 12, No. 1, 39-57 (2019). MSC: 65M70 35R11 PDF BibTeX XML Cite \textit{M. I. Chohan} and \textit{K. Shah}, Eur. J. Pure Appl. Math. 12, No. 1, 39--57 (2019; Zbl 1424.65182) Full Text: Link OpenURL
Maitama, Shehu; Zhao, Weidong Local fractional homotopy analysis method for solving non-differentiable problems on Cantor sets. (English) Zbl 1459.34033 Adv. Difference Equ. 2019, Paper No. 127, 22 p. (2019). MSC: 34A08 65H20 26A33 PDF BibTeX XML Cite \textit{S. Maitama} and \textit{W. Zhao}, Adv. Difference Equ. 2019, Paper No. 127, 22 p. (2019; Zbl 1459.34033) Full Text: DOI OpenURL
Yépez-Martínez, H.; Gómez-Aguilar, J. F. A new modified definition of Caputo-fabrizio fractional-order derivative and their applications to the multi step homotopy analysis method (MHAM). (English) Zbl 1402.26005 J. Comput. Appl. Math. 346, 247-260 (2019). MSC: 26A33 34A08 34A45 65L99 PDF BibTeX XML Cite \textit{H. Yépez-Martínez} and \textit{J. F. Gómez-Aguilar}, J. Comput. Appl. Math. 346, 247--260 (2019; Zbl 1402.26005) Full Text: DOI OpenURL
Firoozjaee, M. A.; Yousefi, S. A. A numerical approach for fractional partial differential equations by using Ritz approximation. (English) Zbl 1427.65245 Appl. Math. Comput. 338, 711-721 (2018). MSC: 65M60 35R11 65M70 35Q53 PDF BibTeX XML Cite \textit{M. A. Firoozjaee} and \textit{S. A. Yousefi}, Appl. Math. Comput. 338, 711--721 (2018; Zbl 1427.65245) Full Text: DOI OpenURL
Zheng, Rumeng; Jiang, Xiaoyun; Zhang, Hui L1 Fourier spectral methods for a class of generalized two-dimensional time fractional nonlinear anomalous diffusion equations. (English) Zbl 1409.65082 Comput. Math. Appl. 75, No. 5, 1515-1530 (2018). MSC: 65M70 65M12 35R11 PDF BibTeX XML Cite \textit{R. Zheng} et al., Comput. Math. Appl. 75, No. 5, 1515--1530 (2018; Zbl 1409.65082) Full Text: DOI OpenURL
Shah, Kamal; Akram, Mohammad Numerical treatment of non-integer order partial differential equations by omitting discretization of data. (English) Zbl 1438.35440 Comput. Appl. Math. 37, No. 5, 6700-6718 (2018). MSC: 35R11 26A33 34A08 35B40 PDF BibTeX XML Cite \textit{K. Shah} and \textit{M. Akram}, Comput. Appl. Math. 37, No. 5, 6700--6718 (2018; Zbl 1438.35440) Full Text: DOI OpenURL
Firoozjaee, M. A.; Jafari, H.; Lia, A.; Baleanu, D. Numerical approach of Fokker-Planck equation with Caputo-Fabrizio fractional derivative using Ritz approximation. (English) Zbl 1393.65029 J. Comput. Appl. Math. 339, 367-373 (2018). MSC: 65M60 35R11 65M12 82C31 35Q84 65H10 26A33 60K10 PDF BibTeX XML Cite \textit{M. A. Firoozjaee} et al., J. Comput. Appl. Math. 339, 367--373 (2018; Zbl 1393.65029) Full Text: DOI OpenURL
Aslan, Ebru Cavlak; Inc, Mustafa; Al Qurashi, Maysaa’ Mohamed; Baleanu, Dumitru On numerical solutions of time-fraction generalized Hirota Satsuma coupled KdV equation. (English) Zbl 1412.34010 J. Nonlinear Sci. Appl. 10, No. 2, 724-733 (2017). MSC: 34A08 26A33 PDF BibTeX XML Cite \textit{E. C. Aslan} et al., J. Nonlinear Sci. Appl. 10, No. 2, 724--733 (2017; Zbl 1412.34010) Full Text: DOI OpenURL
Kazemi, B. Fakhr; Jafari, H. Error estimate of the MQ-RBF collocation method for fractional differential equations with Caputo-Fabrizio derivative. (English) Zbl 1407.65084 Math. Sci., Springer 11, No. 4, 297-305 (2017). MSC: 65L60 34A08 PDF BibTeX XML Cite \textit{B. F. Kazemi} and \textit{H. Jafari}, Math. Sci., Springer 11, No. 4, 297--305 (2017; Zbl 1407.65084) Full Text: DOI OpenURL
Zeid, Samaneh Soradi; Kamyad, Ali Vahidian; Effati, Sohrab; Rakhshan, Seyed Ali; Hosseinpour, Soleiman Numerical solutions for solving a class of fractional optimal control problems via fixed-point approach. (English) Zbl 1381.49031 S\(\vec{\text{e}}\)MA J. 74, No. 4, 585-603 (2017). MSC: 49M25 49L99 65L03 34A08 47H10 PDF BibTeX XML Cite \textit{S. S. Zeid} et al., S\(\vec{\text{e}}\)MA J. 74, No. 4, 585--603 (2017; Zbl 1381.49031) Full Text: DOI OpenURL
Khorshidi, Meisam Noei; Yousefi, Sohrab Ali; Firoozjaee, Mohammad Arab Determination of an unknown source term for an inverse source problem of the time-fractional equation. (English) Zbl 1370.35264 Asian-Eur. J. Math. 10, No. 2, Article ID 1750031, 15 p. (2017). MSC: 35R11 PDF BibTeX XML Cite \textit{M. N. Khorshidi} et al., Asian-Eur. J. Math. 10, No. 2, Article ID 1750031, 15 p. (2017; Zbl 1370.35264) Full Text: DOI OpenURL
Abolhasani, Mohammad; Abbasbandy, Saeid; Allahviranloo, Tofigh A new variational iteration method for a class of fractional convection-diffusion equations in large domains. (English) Zbl 1457.65156 Mathematics 5, No. 2, Paper No. 26, 15 p. (2017). MSC: 65M99 65M12 35R11 PDF BibTeX XML Cite \textit{M. Abolhasani} et al., Mathematics 5, No. 2, Paper No. 26, 15 p. (2017; Zbl 1457.65156) Full Text: DOI OpenURL
Gómez-Aguilar, J. F.; Torres, L.; Yépez-Martínez, H.; Baleanu, D.; Reyes, J. M.; Sosa, I. O. Fractional Liénard type model of a pipeline within the fractional derivative without singular kernel. (English) Zbl 1419.35208 Adv. Difference Equ. 2016, Paper No. 173, 13 p. (2016). MSC: 35R11 34A08 34A25 26A33 65M99 35Q35 PDF BibTeX XML Cite \textit{J. F. Gómez-Aguilar} et al., Adv. Difference Equ. 2016, Paper No. 173, 13 p. (2016; Zbl 1419.35208) Full Text: DOI OpenURL
Morales-Delgado, Victor Fabian; Gómez-Aguilar, José Francisco; Yépez-Martínez, Huitzilin; Baleanu, Dumitru; Escobar-Jimenez, Ricardo Fabricio; Olivares-Peregrino, Victor Hugo Laplace homotopy analysis method for solving linear partial differential equations using a fractional derivative with and without kernel singular. (English) Zbl 1419.35220 Adv. Difference Equ. 2016, Paper No. 164, 17 p. (2016). MSC: 35R11 26A33 34A08 65M99 34A45 PDF BibTeX XML Cite \textit{V. F. Morales-Delgado} et al., Adv. Difference Equ. 2016, Paper No. 164, 17 p. (2016; Zbl 1419.35220) Full Text: DOI OpenURL
Rostamy, D.; Qasemi, S. Discontinuous Petrov-Galerkin and Bernstein-Legendre polynomials method for solving fractional damped heat- and wave-like equations. (English) Zbl 07499223 J. Comput. Theor. Transp. 44, No. 1, 1-23 (2015). MSC: 82-XX PDF BibTeX XML Cite \textit{D. Rostamy} and \textit{S. Qasemi}, J. Comput. Theor. Transp. 44, No. 1, 1--23 (2015; Zbl 07499223) Full Text: DOI OpenURL
Jassim, Hassan Kamil; Ünlü, Canan; Moshokoa, Seithuti Philemon; Khalique, Chaudry Masood Local fractional Laplace variational iteration method for solving diffusion and wave equations on Cantor sets within local fractional operators. (English) Zbl 1394.65119 Math. Probl. Eng. 2015, Article ID 309870, 9 p. (2015). MSC: 65M99 35R11 PDF BibTeX XML Cite \textit{H. K. Jassim} et al., Math. Probl. Eng. 2015, Article ID 309870, 9 p. (2015; Zbl 1394.65119) Full Text: DOI OpenURL
Pirkhedri, A.; Javadi, H. H. S. Solving the time-fractional diffusion equation via sinc-Haar collocation method. (English) Zbl 1339.65193 Appl. Math. Comput. 257, 317-326 (2015). MSC: 65M70 PDF BibTeX XML Cite \textit{A. Pirkhedri} and \textit{H. H. S. Javadi}, Appl. Math. Comput. 257, 317--326 (2015; Zbl 1339.65193) Full Text: DOI OpenURL
Bota, Constantin; Căruntu, Bogdan Approximate analytical solutions of the fractional-order Brusselator system using the polynomial least squares method. (English) Zbl 1338.34044 Adv. Math. Phys. 2015, Article ID 450235, 5 p. (2015). MSC: 34A45 34A08 PDF BibTeX XML Cite \textit{C. Bota} and \textit{B. Căruntu}, Adv. Math. Phys. 2015, Article ID 450235, 5 p. (2015; Zbl 1338.34044) Full Text: DOI OpenURL
Odibat, Zaid; Bataineh, A. Sami An adaptation of homotopy analysis method for reliable treatment of strongly nonlinear problems: construction of homotopy polynomials. (English) Zbl 1318.34021 Math. Methods Appl. Sci. 38, No. 5, 991-1000 (2015). MSC: 34A45 34A12 34A34 41A58 PDF BibTeX XML Cite \textit{Z. Odibat} and \textit{A. S. Bataineh}, Math. Methods Appl. Sci. 38, No. 5, 991--1000 (2015; Zbl 1318.34021) Full Text: DOI OpenURL
Hemeda, A. A. Modified homotopy perturbation method for solving fractional differential equations. (English) Zbl 1442.65318 J. Appl. Math. 2014, Article ID 594245, 9 p. (2014). MSC: 65M99 PDF BibTeX XML Cite \textit{A. A. Hemeda}, J. Appl. Math. 2014, Article ID 594245, 9 p. (2014; Zbl 1442.65318) Full Text: DOI OpenURL
Elbeleze, Asma Ali; Kılıçman, Adem; Taib, Bachok M. Note on the convergence analysis of homotopy perturbation method for fractional partial differential equations. (English) Zbl 1474.65408 Abstr. Appl. Anal. 2014, Article ID 803902, 8 p. (2014). MSC: 65M99 35R11 PDF BibTeX XML Cite \textit{A. A. Elbeleze} et al., Abstr. Appl. Anal. 2014, Article ID 803902, 8 p. (2014; Zbl 1474.65408) Full Text: DOI OpenURL
Jafari, H.; Kadem, Abdelouahab; Baleanu, D. Variational iteration method for a fractional-order Brusselator system. (English) Zbl 1470.34051 Abstr. Appl. Anal. 2014, Article ID 496323, 6 p. (2014). MSC: 34A45 PDF BibTeX XML Cite \textit{H. Jafari} et al., Abstr. Appl. Anal. 2014, Article ID 496323, 6 p. (2014; Zbl 1470.34051) Full Text: DOI OpenURL
Zhao, Chun-Guang; Yang, Ai-Min; Jafari, Hossein; Haghbin, Ahmad The Yang-Laplace transform for solving the IVPs with local fractional derivative. (English) Zbl 1470.34037 Abstr. Appl. Anal. 2014, Article ID 386459, 5 p. (2014). MSC: 34A08 34A25 PDF BibTeX XML Cite \textit{C.-G. Zhao} et al., Abstr. Appl. Anal. 2014, Article ID 386459, 5 p. (2014; Zbl 1470.34037) Full Text: DOI OpenURL
Wang, Shun-Qin; Yang, Yong-Ju; Jassim, Hassan Kamil Local fractional function decomposition method for solving inhomogeneous wave equations with local fractional derivative. (English) Zbl 1470.35416 Abstr. Appl. Anal. 2014, Article ID 176395, 7 p. (2014). MSC: 35R11 PDF BibTeX XML Cite \textit{S.-Q. Wang} et al., Abstr. Appl. Anal. 2014, Article ID 176395, 7 p. (2014; Zbl 1470.35416) Full Text: DOI OpenURL
Wang, Xian-Jin; Zhao, Yang; Cattani, Carlo; Yang, Xiao-Jun Local fractional variational iteration method for inhomogeneous Helmholtz equation within local fractional derivative operator. (English) Zbl 1407.65320 Math. Probl. Eng. 2014, Article ID 913202, 7 p. (2014). MSC: 65N99 35R11 PDF BibTeX XML Cite \textit{X.-J. Wang} et al., Math. Probl. Eng. 2014, Article ID 913202, 7 p. (2014; Zbl 1407.65320) Full Text: DOI OpenURL
Atangana, Abdon; Oukouomi Noutchie, Suares Clovis On multi-Laplace transform for solving nonlinear partial differential equations with mixed derivatives. (English) Zbl 1407.35058 Math. Probl. Eng. 2014, Article ID 267843, 9 p. (2014). MSC: 35G20 35A22 35C05 35R11 PDF BibTeX XML Cite \textit{A. Atangana} and \textit{S. C. Oukouomi Noutchie}, Math. Probl. Eng. 2014, Article ID 267843, 9 p. (2014; Zbl 1407.35058) Full Text: DOI OpenURL
Zhang, Yue; Wang, Kuanquan; Yuan, Yongfeng; Sui, Dong; Zhang, Henggui Effects of maximal sodium and potassium conductance on the stability of Hodgkin-Huxley model. (English) Zbl 1307.92073 Comput. Math. Methods Med. 2014, Article ID 761907, 9 p. (2014). MSC: 92C37 PDF BibTeX XML Cite \textit{Y. Zhang} et al., Comput. Math. Methods Med. 2014, Article ID 761907, 9 p. (2014; Zbl 1307.92073) Full Text: DOI OpenURL
Li, Yang; Wang, Long-Fei; Zeng, Sheng-Da; Zhao, Yang Local fractional Laplace variational iteration method for fractal vehicular traffic flow. (English) Zbl 1348.35295 Adv. Math. Phys. 2014, Article ID 649318, 7 p. (2014). MSC: 35R11 65M99 90B20 PDF BibTeX XML Cite \textit{Y. Li} et al., Adv. Math. Phys. 2014, Article ID 649318, 7 p. (2014; Zbl 1348.35295) Full Text: DOI OpenURL
El-Danaf, Talaat S.; Hadhoud, Adel R. Computational method for solving space fractional Fisher’s nonlinear equation. (English) Zbl 1288.65147 Math. Methods Appl. Sci. 37, No. 5, 657-662 (2014). MSC: 65M70 35R11 35K55 65M12 PDF BibTeX XML Cite \textit{T. S. El-Danaf} and \textit{A. R. Hadhoud}, Math. Methods Appl. Sci. 37, No. 5, 657--662 (2014; Zbl 1288.65147) Full Text: DOI OpenURL
Liu, Xiao-jing; Wang, Ji-zeng; Wang, Xiao-min; Zhou, You-he Exact solutions of multi-term fractional diffusion-wave equations with Robin type boundary conditions. (English) Zbl 1284.35455 Appl. Math. Mech., Engl. Ed. 35, No. 1, 49-62 (2014). MSC: 35R11 34A08 44A10 65T60 PDF BibTeX XML Cite \textit{X.-j. Liu} et al., Appl. Math. Mech., Engl. Ed. 35, No. 1, 49--62 (2014; Zbl 1284.35455) Full Text: DOI OpenURL
Bulut, Hasan; Baskonus, Haci Mehmet; Pandir, Yusuf The modified trial equation method for fractional wave equation and time fractional generalized Burgers equation. (English) Zbl 1470.35390 Abstr. Appl. Anal. 2013, Article ID 636802, 8 p. (2013). MSC: 35R11 35Q53 PDF BibTeX XML Cite \textit{H. Bulut} et al., Abstr. Appl. Anal. 2013, Article ID 636802, 8 p. (2013; Zbl 1470.35390) Full Text: DOI OpenURL
Damor, R. S.; Kumar, Sushil; Shukla, A. K. Numerical solution of fractional diffusion equation model for freezing in finite media. (English) Zbl 1381.76256 Int. J. Eng. Math. 2013, Article ID 785609, 8 p. (2013). MSC: 76M25 35Q35 35R11 76T99 PDF BibTeX XML Cite \textit{R. S. Damor} et al., Int. J. Eng. Math. 2013, Article ID 785609, 8 p. (2013; Zbl 1381.76256) Full Text: DOI OpenURL
Su, Wei-Hua; Baleanu, Dumitru; Yang, Xiao-Jun; Jafari, Hossein Damped wave equation and dissipative wave equation in fractal strings within the local fractional variational iteration method. (English) Zbl 1291.74083 Fixed Point Theory Appl. 2013, Paper No. 89, 11 p. (2013). MSC: 74H10 35L05 28A80 PDF BibTeX XML Cite \textit{W.-H. Su} et al., Fixed Point Theory Appl. 2013, Paper No. 89, 11 p. (2013; Zbl 1291.74083) Full Text: DOI OpenURL
Yang, Yong-Ju; Baleanu, Dumitru; Yang, Xiao-Jun Analysis of fractal wave equations by local fractional Fourier series method. (English) Zbl 1291.35123 Adv. Math. Phys. 2013, Article ID 632309, 6 p. (2013). MSC: 35L05 35R11 PDF BibTeX XML Cite \textit{Y.-J. Yang} et al., Adv. Math. Phys. 2013, Article ID 632309, 6 p. (2013; Zbl 1291.35123) Full Text: DOI OpenURL
Zhao, Yang; Cheng, De-Fu; Yang, Xiao-Jun Approximation solutions for local fractional Schrödinger equation in the one-dimensional Cantorian system. (English) Zbl 1292.81050 Adv. Math. Phys. 2013, Article ID 291386, 5 p. (2013). MSC: 81Q05 34A08 81Q35 81Q15 26A33 PDF BibTeX XML Cite \textit{Y. Zhao} et al., Adv. Math. Phys. 2013, Article ID 291386, 5 p. (2013; Zbl 1292.81050) Full Text: DOI OpenURL
Yang, Ai-Min; Yang, Xiao-Jun; Li, Zheng-Biao Local fractional series expansion method for solving wave and diffusion equations on Cantor sets. (English) Zbl 1295.35178 Abstr. Appl. Anal. 2013, Article ID 351057, 5 p. (2013). MSC: 35C10 35K10 35L10 35R11 PDF BibTeX XML Cite \textit{A.-M. Yang} et al., Abstr. Appl. Anal. 2013, Article ID 351057, 5 p. (2013; Zbl 1295.35178) Full Text: DOI OpenURL
Płociniczak, Łukasz; Okrasińska, Hanna Approximate self-similar solutions to a nonlinear diffusion equation with time-fractional derivative. (English) Zbl 1286.35060 Physica D 261, 85-91 (2013). MSC: 35C06 35R11 35K55 35K65 PDF BibTeX XML Cite \textit{Ł. Płociniczak} and \textit{H. Okrasińska}, Physica D 261, 85--91 (2013; Zbl 1286.35060) Full Text: DOI OpenURL
Hariharan, G. The homotopy analysis method applied to the Kolmogorov-Petrovskii-Piskunov (KPP) and fractional KPP equations. (English) Zbl 1402.92456 J. Math. Chem. 51, No. 3, 992-1000 (2013). MSC: 92E20 26A33 PDF BibTeX XML Cite \textit{G. Hariharan}, J. Math. Chem. 51, No. 3, 992--1000 (2013; Zbl 1402.92456) Full Text: DOI OpenURL
Kurulay, Muhammet Solving the fractional nonlinear Klein-Gordon equation by means of the homotopy analysis method. (English) Zbl 1377.35270 Adv. Difference Equ. 2012, Paper No. 187, 8 p. (2012). MSC: 35R11 35G20 33E12 65M99 PDF BibTeX XML Cite \textit{M. Kurulay}, Adv. Difference Equ. 2012, Paper No. 187, 8 p. (2012; Zbl 1377.35270) Full Text: DOI OpenURL
Rostamy, Davood; Karimi, Kobra Bernstein polynomials for solving fractional heat- and wave-like equations. (English) Zbl 1312.65168 Fract. Calc. Appl. Anal. 15, No. 4, 556-571 (2012). MSC: 65M70 35R11 26A33 41A10 45K05 41A30 PDF BibTeX XML Cite \textit{D. Rostamy} and \textit{K. Karimi}, Fract. Calc. Appl. Anal. 15, No. 4, 556--571 (2012; Zbl 1312.65168) Full Text: DOI OpenURL
Hu, Ming-Sheng; Agarwal, Ravi P.; Yang, Xiao-Jun Local fractional Fourier series with application to wave equation in fractal vibrating string. (English) Zbl 1257.35193 Abstr. Appl. Anal. 2012, Article ID 567401, 15 p. (2012). MSC: 35R11 33E12 81Q35 PDF BibTeX XML Cite \textit{M.-S. Hu} et al., Abstr. Appl. Anal. 2012, Article ID 567401, 15 p. (2012; Zbl 1257.35193) Full Text: DOI OpenURL
Hesameddini, Esmail; Latifizadeh, Habibolla Homotopy analysis method to obtain numerical solutions of the Painlevé equations. (English) Zbl 1252.34020 Math. Methods Appl. Sci. 35, No. 12, 1423-1433 (2012). MSC: 34A45 34M55 34A25 PDF BibTeX XML Cite \textit{E. Hesameddini} and \textit{H. Latifizadeh}, Math. Methods Appl. Sci. 35, No. 12, 1423--1433 (2012; Zbl 1252.34020) Full Text: DOI OpenURL
İbiş, Birol; Bayram, Mustafa; Ağargün, A. Göksel Applications of fractional differential transform method to fractional differential-algebraic equations. (English) Zbl 1389.34016 Eur. J. Pure Appl. Math. 4, No. 2, 129-141 (2011). MSC: 34A08 34A09 34A25 34A45 PDF BibTeX XML Cite \textit{B. İbiş} et al., Eur. J. Pure Appl. Math. 4, No. 2, 129--141 (2011; Zbl 1389.34016) Full Text: Link OpenURL
Jafari, H.; Tajadodi, H.; Biswas, Anjan Homotopy analysis method for solving a couple of evolution equations and comparison with Adomian’s decomposition method. (English) Zbl 1274.35046 Waves Random Complex Media 21, No. 4, 657-667 (2011). MSC: 35C10 PDF BibTeX XML Cite \textit{H. Jafari} et al., Waves Random Complex Media 21, No. 4, 657--667 (2011; Zbl 1274.35046) Full Text: DOI OpenURL
Hu, Xiuling; Zhang, Luming A compact finite difference scheme for the fourth-order fractional diffusion-wave system. (English) Zbl 1262.65102 Comput. Phys. Commun. 182, No. 8, 1645-1650 (2011). MSC: 65M06 35R11 35K35 65M12 PDF BibTeX XML Cite \textit{X. Hu} and \textit{L. Zhang}, Comput. Phys. Commun. 182, No. 8, 1645--1650 (2011; Zbl 1262.65102) Full Text: DOI OpenURL
Vanani, S. Karimi; Aminataei, A. Tau approximate solution of fractional partial differential equations. (English) Zbl 1228.65205 Comput. Math. Appl. 62, No. 3, 1075-1083 (2011). MSC: 65M99 35R11 26A33 45K05 PDF BibTeX XML Cite \textit{S. K. Vanani} and \textit{A. Aminataei}, Comput. Math. Appl. 62, No. 3, 1075--1083 (2011; Zbl 1228.65205) Full Text: DOI OpenURL
Abbasbandy, S.; López, J. L.; López-Ruiz, R. The homotopy analysis method and the Liénard equation. (English) Zbl 1211.65088 Int. J. Comput. Math. 88, No. 1, 121-134 (2011). MSC: 65L05 65L60 34M10 34C07 PDF BibTeX XML Cite \textit{S. Abbasbandy} et al., Int. J. Comput. Math. 88, No. 1, 121--134 (2011; Zbl 1211.65088) Full Text: DOI arXiv OpenURL
Kurulay, Muhammet; Bayram, Mustafa Approximate analytical solution for the fractional modified Kdv by differential transform method. (English) Zbl 1222.35172 Commun. Nonlinear Sci. Numer. Simul. 15, No. 7, 1777-1782 (2010). MSC: 35Q53 PDF BibTeX XML Cite \textit{M. Kurulay} and \textit{M. Bayram}, Commun. Nonlinear Sci. Numer. Simul. 15, No. 7, 1777--1782 (2010; Zbl 1222.35172) Full Text: DOI OpenURL
Odibat, Zaid M. A study on the convergence of homotopy analysis method. (English) Zbl 1203.65105 Appl. Math. Comput. 217, No. 2, 782-789 (2010). Reviewer: Werner M. Seiler (Kassel) MSC: 65L05 41A58 34A25 34A34 65L70 PDF BibTeX XML Cite \textit{Z. M. Odibat}, Appl. Math. Comput. 217, No. 2, 782--789 (2010; Zbl 1203.65105) Full Text: DOI OpenURL
Zhu, Hongqing; Shu, Huazhong; Ding, Meiyu Numerical solutions of partial differential equations by discrete homotopy analysis method. (English) Zbl 1195.65143 Appl. Math. Comput. 216, No. 12, 3592-3605 (2010). MSC: 65M70 35K05 35Q53 65M12 PDF BibTeX XML Cite \textit{H. Zhu} et al., Appl. Math. Comput. 216, No. 12, 3592--3605 (2010; Zbl 1195.65143) Full Text: DOI OpenURL
Bai, Chuanzhi Existence of positive solutions for a functional fractional boundary value problem. (English) Zbl 1197.34156 Abstr. Appl. Anal. 2010, Article ID 127363, 13 p. (2010). MSC: 34K37 34K10 PDF BibTeX XML Cite \textit{C. Bai}, Abstr. Appl. Anal. 2010, Article ID 127363, 13 p. (2010; Zbl 1197.34156) Full Text: DOI EuDML OpenURL
Jafari, H.; Golbabai, A.; Seifi, S.; Sayevand, K. Homotopy analysis method for solving multi-term linear and nonlinear diffusion-wave equations of fractional order. (English) Zbl 1189.65250 Comput. Math. Appl. 59, No. 3, 1337-1344 (2010). MSC: 65M99 26A33 35R11 45K05 PDF BibTeX XML Cite \textit{H. Jafari} et al., Comput. Math. Appl. 59, No. 3, 1337--1344 (2010; Zbl 1189.65250) Full Text: DOI OpenURL
Zurigat, Mohammad; Momani, Shaher; Alawneh, Ahmad Analytical approximate solutions of systems of fractional algebraic-differential equations by homotopy analysis method. (English) Zbl 1189.65187 Comput. Math. Appl. 59, No. 3, 1227-1235 (2010). MSC: 65L99 26A33 34A08 34A09 34A45 PDF BibTeX XML Cite \textit{M. Zurigat} et al., Comput. Math. Appl. 59, No. 3, 1227--1235 (2010; Zbl 1189.65187) Full Text: DOI OpenURL
Dehghan, Mehdi; Manafian, Jalil; Saadatmandi, Abbas Solving nonlinear fractional partial differential equations using the homotopy analysis method. (English) Zbl 1185.65187 Numer. Methods Partial Differ. Equations 26, No. 2, 448-479 (2010). MSC: 65M70 35R11 35Q53 35C10 PDF BibTeX XML Cite \textit{M. Dehghan} et al., Numer. Methods Partial Differ. Equations 26, No. 2, 448--479 (2010; Zbl 1185.65187) Full Text: DOI OpenURL
Jafari, H.; Seifi, S. Solving a system of nonlinear fractional partial differential equations using homotopy analysis method. (English) Zbl 1221.35439 Commun. Nonlinear Sci. Numer. Simul. 14, No. 5, 1962-1969 (2009). MSC: 35R11 26A33 35G10 35G15 PDF BibTeX XML Cite \textit{H. Jafari} and \textit{S. Seifi}, Commun. Nonlinear Sci. Numer. Simul. 14, No. 5, 1962--1969 (2009; Zbl 1221.35439) Full Text: DOI OpenURL
Van Gorder, Robert A.; Vajravelu, K. On the selection of auxiliary functions, operators, and convergence control parameters in the application of the homotopy analysis method to nonlinear differential equations: a general approach. (English) Zbl 1221.65208 Commun. Nonlinear Sci. Numer. Simul. 14, No. 12, 4078-4089 (2009). MSC: 65L99 PDF BibTeX XML Cite \textit{R. A. Van Gorder} and \textit{K. Vajravelu}, Commun. Nonlinear Sci. Numer. Simul. 14, No. 12, 4078--4089 (2009; Zbl 1221.65208) Full Text: DOI OpenURL
Belmekki, Mohammed; Nieto, Juan J.; Rodríguez-López, Rosana Existence of periodic solution for a nonlinear fractional differential equation. (English) Zbl 1181.34006 Bound. Value Probl. 2009, Article ID 324561, 18 p. (2009). MSC: 34A08 34C25 34B15 PDF BibTeX XML Cite \textit{M. Belmekki} et al., Bound. Value Probl. 2009, Article ID 324561, 18 p. (2009; Zbl 1181.34006) Full Text: DOI OpenURL
Ahmad, Bashir; Nieto, Juan J. Existence results for nonlinear boundary value problems of fractional integrodifferential equations with integral boundary conditions. (English) Zbl 1167.45003 Bound. Value Probl. 2009, Article ID 708576, 11 p. (2009). MSC: 45J05 45G10 26A33 PDF BibTeX XML Cite \textit{B. Ahmad} and \textit{J. J. Nieto}, Bound. Value Probl. 2009, Article ID 708576, 11 p. (2009; Zbl 1167.45003) Full Text: DOI EuDML OpenURL
Abdulaziz, O.; Hashim, I.; Saif, A. Series solutions of time-fractional PDEs by homotopy analysis method. (English) Zbl 1172.35305 Differ. Equ. Nonlinear Mech. 2008, Article ID 686512, 16 p. (2008). MSC: 35A25 26A33 35C10 35S05 PDF BibTeX XML Cite \textit{O. Abdulaziz} et al., Differ. Equ. Nonlinear Mech. 2008, Article ID 686512, 16 p. (2008; Zbl 1172.35305) Full Text: DOI EuDML OpenURL