Shukla, Shitesh; Kumar, Mukesh Numerical simulation of time and space fractional partial differential equation via 3-scale Haar wavelet. (English) Zbl 07549900 Int. J. Appl. Comput. Math. 8, No. 4, Paper No. 160, 19 p. (2022). MSC: 65-XX 35-XX PDF BibTeX XML Cite \textit{S. Shukla} and \textit{M. Kumar}, Int. J. Appl. Comput. Math. 8, No. 4, Paper No. 160, 19 p. (2022; Zbl 07549900) Full Text: DOI OpenURL
Su, Lingde; Huang, Jian; Vasil’ev, V. I.; Li, Ao; Kardashevsky, A. M. A numerical method for solving retrospective inverse problem of fractional parabolic equation. (English) Zbl 07542688 J. Comput. Appl. Math. 413, Article ID 114366, 11 p. (2022). MSC: 65M30 35R11 65M32 PDF BibTeX XML Cite \textit{L. Su} et al., J. Comput. Appl. Math. 413, Article ID 114366, 11 p. (2022; Zbl 07542688) Full Text: DOI OpenURL
Zhang, Qifeng; Liu, Lingling; Zhang, Chengjian Compact scheme for fractional diffusion-wave equation with spatial variable coefficient and delays. (English) Zbl 07518214 Appl. Anal. 101, No. 6, 1911-1932 (2022). MSC: 65M06 65M12 PDF BibTeX XML Cite \textit{Q. Zhang} et al., Appl. Anal. 101, No. 6, 1911--1932 (2022; Zbl 07518214) Full Text: DOI OpenURL
Farid, S.; Nawaz, R.; Shah, Zahir; Islam, Saeed; Deebani, Wejdan New iterative transform method for time and space fractional \((n+1)\)-dimensional heat and wave type equations. (English) Zbl 07465399 Fractals 29, No. 3, Article ID 2150056, 15 p. (2021). MSC: 65-XX 35-XX PDF BibTeX XML Cite \textit{S. Farid} et al., Fractals 29, No. 3, Article ID 2150056, 15 p. (2021; Zbl 07465399) Full Text: DOI OpenURL
Gubes, Murat; Keskin, Yildiray; Oturanc, Galip Numerical solutions of nonlinear wave-like equations by reduced differential transform method. (English) Zbl 1483.65168 Thai J. Math. 18, No. 2, 639-650 (2020). MSC: 65M99 35A25 35G20 35L75 PDF BibTeX XML Cite \textit{M. Gubes} et al., Thai J. Math. 18, No. 2, 639--650 (2020; Zbl 1483.65168) Full Text: arXiv Link OpenURL
Saw, Vijay; Kumar, Sushil Collocation method for time fractional diffusion equation based on the Chebyshev polynomials of second kind. (English) Zbl 1466.65158 Int. J. Appl. Comput. Math. 6, No. 4, Paper No. 117, 13 p. (2020). MSC: 65M70 65M06 65M12 65M15 35R11 PDF BibTeX XML Cite \textit{V. Saw} and \textit{S. Kumar}, Int. J. Appl. Comput. Math. 6, No. 4, Paper No. 117, 13 p. (2020; Zbl 1466.65158) Full Text: DOI OpenURL
Sabermahani, Sedigheh; Ordokhani, Yadollah; Yousefi, Sohrab-Ali Two-dimensional Müntz-Legendre hybrid functions: theory and applications for solving fractional-order partial differential equations. (English) Zbl 1449.65278 Comput. Appl. Math. 39, No. 2, Paper No. 111, 22 p. (2020). MSC: 65M70 65N35 35R11 26A33 65H10 42C10 PDF BibTeX XML Cite \textit{S. Sabermahani} et al., Comput. Appl. Math. 39, No. 2, Paper No. 111, 22 p. (2020; Zbl 1449.65278) Full Text: DOI OpenURL
Kumar, Devendra; Singh, Jagdev; Purohit, Sunil Dutt; Swroop, Ram A hybrid analytical algorithm for nonlinear fractional wave-like equations. (English) Zbl 1423.65001 Math. Model. Nat. Phenom. 14, No. 3, Paper No. 304, 13 p. (2019). MSC: 65M99 35R11 35L05 PDF BibTeX XML Cite \textit{D. Kumar} et al., Math. Model. Nat. Phenom. 14, No. 3, Paper No. 304, 13 p. (2019; Zbl 1423.65001) 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
Singh, Brajesh Kumar Homotopy perturbation new integral transform method for numeric study of space- and time-fractional \((n+1)\)-dimensional heat- and wave-like equations. (English) Zbl 1431.65196 Waves Wavelets Fractals, Adv. Anal. 4, 19-36 (2018). MSC: 65M99 35R11 35C10 PDF BibTeX XML Cite \textit{B. K. Singh}, Waves Wavelets Fractals, Adv. Anal. 4, 19--36 (2018; Zbl 1431.65196) 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
Zheng, Yunying; Zhao, Zhengang The discontinuous Galerkin finite element method for fractional cable equation. (English) Zbl 1358.65083 Appl. Numer. Math. 115, 32-41 (2017). MSC: 65R20 35Q84 35Q92 45J05 45G15 35R11 PDF BibTeX XML Cite \textit{Y. Zheng} and \textit{Z. Zhao}, Appl. Numer. Math. 115, 32--41 (2017; Zbl 1358.65083) Full Text: DOI OpenURL
Singh, J.; Kumar, D.; Swroop, R.; Kumar, S. Numerical computation of fractional partial differential equations arising in physics. (English) Zbl 1474.34052 J. Niger. Math. Soc. 35, No. 3, 439-459 (2016). MSC: 34A08 35A20 35A22 PDF BibTeX XML Cite \textit{J. Singh} et al., J. Niger. Math. Soc. 35, No. 3, 439--459 (2016; Zbl 1474.34052) Full Text: Link OpenURL
Bhrawy, Ali; Zaky, Mahmoud A fractional-order Jacobi tau method for a class of time-fractional PDEs with variable coefficients. (English) Zbl 1382.65338 Math. Methods Appl. Sci. 39, No. 7, 1765-1779 (2016). MSC: 65M70 35R11 PDF BibTeX XML Cite \textit{A. Bhrawy} and \textit{M. Zaky}, Math. Methods Appl. Sci. 39, No. 7, 1765--1779 (2016; Zbl 1382.65338) 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
Sarwar, S.; Alkhalaf, Salem; Iqbal, S.; Zahid, Manzoor A. A note on optimal homotopy asymptotic method for the solutions of fractional order heat- and wave-like partial differential equations. (English) Zbl 1443.35174 Comput. Math. Appl. 70, No. 5, 942-953 (2015). MSC: 35R11 PDF BibTeX XML Cite \textit{S. Sarwar} et al., Comput. Math. Appl. 70, No. 5, 942--953 (2015; Zbl 1443.35174) Full Text: DOI OpenURL
Biala, T. A.; Jator, S. N. Block implicit Adams methods for fractional differential equations. (English) Zbl 1355.65094 Chaos Solitons Fractals 81, Part A, 365-377 (2015). MSC: 65L06 65L20 34A08 34K37 PDF BibTeX XML Cite \textit{T. A. Biala} and \textit{S. N. Jator}, Chaos Solitons Fractals 81, Part A, 365--377 (2015; Zbl 1355.65094) 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
Biala, T. A.; Jator, S. N. Block backward differentiation formulas for fractional differential equations. (English) Zbl 1382.65460 Int. J. Eng. Math. 2015, Article ID 650425, 14 p. (2015). MSC: 65N99 35R11 PDF BibTeX XML Cite \textit{T. A. Biala} and \textit{S. N. Jator}, Int. J. Eng. Math. 2015, Article ID 650425, 14 p. (2015; Zbl 1382.65460) Full Text: DOI OpenURL
Izadkhah, Mohammad Mahdi; Saberi-Nadjafi, Jafar Gegenbauer spectral method for time-fractional convection-diffusion equations with variable coefficients. (English) Zbl 1329.35334 Math. Methods Appl. Sci. 38, No. 15, 3183-3194 (2015). MSC: 35R11 65M70 65N22 PDF BibTeX XML Cite \textit{M. M. Izadkhah} and \textit{J. Saberi-Nadjafi}, Math. Methods Appl. Sci. 38, No. 15, 3183--3194 (2015; Zbl 1329.35334) Full Text: DOI OpenURL
Jacobs, B. A.; Harley, C. Two hybrid methods for solving two-dimensional linear time-fractional partial differential equations. (English) Zbl 1474.65389 Abstr. Appl. Anal. 2014, Article ID 757204, 10 p. (2014). MSC: 65M70 65M06 35R11 PDF BibTeX XML Cite \textit{B. A. Jacobs} and \textit{C. Harley}, Abstr. Appl. Anal. 2014, Article ID 757204, 10 p. (2014; Zbl 1474.65389) Full Text: DOI OpenURL
Abbas, Muhammad; Majid, Ahmad Abd.; Ismail, Ahmad Izani Md.; Rashid, Abdur The application of cubic trigonometric B-spline to the numerical solution of the hyperbolic problems. (English) Zbl 1334.65163 Appl. Math. Comput. 239, 74-88 (2014). MSC: 65M70 65M12 PDF BibTeX XML Cite \textit{M. Abbas} et al., Appl. Math. Comput. 239, 74--88 (2014; Zbl 1334.65163) 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
Yin, Fukang; Song, Junqiang; Cao, Xiaoqun A general iteration formula of VIM for fractional heat- and wave-like equations. (English) Zbl 1266.35142 J. Appl. Math. 2013, Article ID 428079, 9 p. (2013). MSC: 35R11 35A15 PDF BibTeX XML Cite \textit{F. Yin} et al., J. Appl. Math. 2013, Article ID 428079, 9 p. (2013; Zbl 1266.35142) Full Text: DOI OpenURL
Bushnaq, Samia; Momani, Shaher; Zhou, Yong A reproducing kernel Hilbert space method for solving integro-differential equations of fractional order. (English) Zbl 1273.65194 J. Optim. Theory Appl. 156, No. 1, 96-105 (2013). Reviewer: Ivan Secrieru (Chişinău) MSC: 65R20 26A33 45G10 45J05 46E22 PDF BibTeX XML Cite \textit{S. Bushnaq} et al., J. Optim. Theory Appl. 156, No. 1, 96--105 (2013; Zbl 1273.65194) Full Text: DOI OpenURL
Secer, Aydin Approximate analytic solution of fractional heat-like and wave-like equations with variable coefficients using the differential transforms method. (English) Zbl 1377.35278 Adv. Difference Equ. 2012, Paper No. 198, 10 p. (2012). MSC: 35R11 35A22 PDF BibTeX XML Cite \textit{A. Secer}, Adv. Difference Equ. 2012, Paper No. 198, 10 p. (2012; Zbl 1377.35278) 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
Khan, Yasir; Wu, Qingbiao; Faraz, Naeem; Yildirim, A.; Madani, M. A new fractional analytical approach via a modified Riemann-Liouville derivative. (English) Zbl 1251.65101 Appl. Math. Lett. 25, No. 10, 1340-1346 (2012). MSC: 65L05 34A08 34A34 PDF BibTeX XML Cite \textit{Y. Khan} et al., Appl. Math. Lett. 25, No. 10, 1340--1346 (2012; Zbl 1251.65101) Full Text: DOI OpenURL
Saadatmandi, Abbas; Dehghan, Mehdi; Azizi, Mohammad-Reza The sinc-Legendre collocation method for a class of fractional convection-diffusion equations with variable coefficients. (English) Zbl 1250.65121 Commun. Nonlinear Sci. Numer. Simul. 17, No. 11, 4125-4136 (2012). MSC: 65M70 35K05 35R11 PDF BibTeX XML Cite \textit{A. Saadatmandi} et al., Commun. Nonlinear Sci. Numer. Simul. 17, No. 11, 4125--4136 (2012; Zbl 1250.65121) Full Text: DOI OpenURL
Al-Rabtah, Adel; Momani, Shaher; Ramadan, Mohamed A. Solving linear and nonlinear fractional differential equations using spline functions. (English) Zbl 1235.65015 Abstr. Appl. Anal. 2012, Article ID 426514, 9 p. (2012). MSC: 65D07 65L99 34A08 PDF BibTeX XML Cite \textit{A. Al-Rabtah} et al., Abstr. Appl. Anal. 2012, Article ID 426514, 9 p. (2012; Zbl 1235.65015) Full Text: DOI OpenURL
Radwan, A. G.; Moaddy, K.; Momani, Shaher Stability and non-standard finite difference method of the generalized Chua’s circuit. (English) Zbl 1228.65120 Comput. Math. Appl. 62, No. 3, 961-970 (2011). MSC: 65L12 34A08 26A33 45J05 94C05 PDF BibTeX XML Cite \textit{A. G. Radwan} et al., Comput. Math. Appl. 62, No. 3, 961--970 (2011; Zbl 1228.65120) Full Text: DOI OpenURL
Moaddy, K.; Momani, S.; Hashim, I. The non-standard finite difference scheme for linear fractional PDEs in fluid mechanics. (English) Zbl 1217.65174 Comput. Math. Appl. 61, No. 4, 1209-1216 (2011). MSC: 65M06 26A33 35Q35 35R11 45K05 76M20 PDF BibTeX XML Cite \textit{K. Moaddy} et al., Comput. Math. Appl. 61, No. 4, 1209--1216 (2011; Zbl 1217.65174) Full Text: DOI OpenURL
Roul, Pradip Numerical solutions of time fractional degenerate parabolic equations by variational iteration method with Jumarie-modified Riemann-Liouville derivative. (English) Zbl 1218.35015 Math. Methods Appl. Sci. 34, No. 9, 1025-1035 (2011). MSC: 35A35 35A20 35A15 35K57 35K65 35R11 35Q92 PDF BibTeX XML Cite \textit{P. Roul}, Math. Methods Appl. Sci. 34, No. 9, 1025--1035 (2011; Zbl 1218.35015) 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. Homotopy analysis method for solving linear and nonlinear fractional diffusion-wave equation. (English) Zbl 1221.65278 Commun. Nonlinear Sci. Numer. Simul. 14, No. 5, 2006-2012 (2009). MSC: 65M99 35G15 PDF BibTeX XML Cite \textit{H. Jafari} and \textit{S. Seifi}, Commun. Nonlinear Sci. Numer. Simul. 14, No. 5, 2006--2012 (2009; Zbl 1221.65278) Full Text: DOI OpenURL
Xu, Hang; Liao, Shi-Jun; You, Xiang-Cheng Analysis of nonlinear fractional partial differential equations with the homotopy analysis method. (English) Zbl 1221.65286 Commun. Nonlinear Sci. Numer. Simul. 14, No. 4, 1152-1156 (2009). MSC: 65M99 35K20 35R11 PDF BibTeX XML Cite \textit{H. Xu} et al., Commun. Nonlinear Sci. Numer. Simul. 14, No. 4, 1152--1156 (2009; Zbl 1221.65286) Full Text: DOI OpenURL
Cang, Jie; Tan, Yue; Xu, Hang; Liao, Shi-Jun Series solutions of non-linear Riccati differential equations with fractional order. (English) Zbl 1197.34006 Chaos Solitons Fractals 40, No. 1, 1-9 (2009). MSC: 34A25 34A08 26A33 PDF BibTeX XML Cite \textit{J. Cang} et al., Chaos Solitons Fractals 40, No. 1, 1--9 (2009; Zbl 1197.34006) Full Text: DOI OpenURL
R, Yulita Molliq; Noorani, M. S. M.; Hashim, I. Variational iteration method for fractional heat- and wave-like equations. (English) Zbl 1172.35302 Nonlinear Anal., Real World Appl. 10, No. 3, 1854-1869 (2009). Reviewer: Samir B. Hadid (Ajman) MSC: 35A15 26A33 35A35 35A25 PDF BibTeX XML Cite \textit{Y. M. R} et al., Nonlinear Anal., Real World Appl. 10, No. 3, 1854--1869 (2009; Zbl 1172.35302) Full Text: DOI OpenURL
Momani, Shaher; Odibat, Zaid A novel method for nonlinear fractional partial differential equations: Combination of DTM and generalized Taylor’s formula. (English) Zbl 1148.65099 J. Comput. Appl. Math. 220, No. 1-2, 85-95 (2008). Reviewer: Kai Diethelm (Braunschweig) MSC: 65R20 65M12 45K05 45G10 65M70 PDF BibTeX XML Cite \textit{S. Momani} and \textit{Z. Odibat}, J. Comput. Appl. Math. 220, No. 1--2, 85--95 (2008; Zbl 1148.65099) Full Text: DOI OpenURL
Inc, Mustafa The approximate and exact solutions of the space- and time-fractional Burgers equations with initial conditions by variational iteration method. (English) Zbl 1146.35304 J. Math. Anal. Appl. 345, No. 1, 476-484 (2008). MSC: 35A35 35S10 26A33 PDF BibTeX XML Cite \textit{M. Inc}, J. Math. Anal. Appl. 345, No. 1, 476--484 (2008; Zbl 1146.35304) Full Text: DOI OpenURL
Zhuang, P.; Liu, Fawang Implicit difference approximation for the two-dimensional space-time fractional diffusion equation. (English) Zbl 1144.65090 J. Appl. Math. Comput. 25, No. 1-2, 269-282 (2007). Reviewer: Vladimir Gorbunov (Ul’yanovsk) MSC: 65R20 26A33 45K05 65M06 65M12 PDF BibTeX XML Cite \textit{P. Zhuang} and \textit{F. Liu}, J. Appl. Math. Comput. 25, No. 1--2, 269--282 (2007; Zbl 1144.65090) Full Text: DOI OpenURL
Momani, Shaher An algorithm for solving the fractional convection-diffusion equation with nonlinear source term. (English) Zbl 1118.35301 Commun. Nonlinear Sci. Numer. Simul. 12, No. 7, 1283-1290 (2007). MSC: 35A25 35K60 35A35 26A33 PDF BibTeX XML Cite \textit{S. Momani}, Commun. Nonlinear Sci. Numer. Simul. 12, No. 7, 1283--1290 (2007; Zbl 1118.35301) Full Text: DOI OpenURL