Khosravian-Arab, Hassan; Dehghan, Mehdi The sine and cosine diffusive representations for the Caputo fractional derivative. arXiv:2309.04005 Preprint, arXiv:2309.04005 [math.NA] (2023). MSC: 26A33 65D30 65D25 65D32 BibTeX Cite \textit{H. Khosravian-Arab} and \textit{M. Dehghan}, ``The sine and cosine diffusive representations for the Caputo fractional derivative'', Preprint, arXiv:2309.04005 [math.NA] (2023) Full Text: arXiv OA License
Dehghan, Mehdi; Ebrahimijahan, Ali; Abbaszadeh, Mostafa Integrated radial basis functions to simulate modified anomalous sub-diffusion equation. (English) Zbl 07778283 Numer. Methods Partial Differ. Equations 38, No. 4, 1015-1054 (2022). MSC: 65M06 65N35 65D12 65M12 60K50 26A33 35R11 PDFBibTeX XMLCite \textit{M. Dehghan} et al., Numer. Methods Partial Differ. Equations 38, No. 4, 1015--1054 (2022; Zbl 07778283) Full Text: DOI
Abbaszadeh, Mostafa; Dehghan, Mehdi A Galerkin meshless reproducing kernel particle method for numerical solution of neutral delay time-space distributed-order fractional damped diffusion-wave equation. (English) Zbl 1486.65157 Appl. Numer. Math. 169, 44-63 (2021). MSC: 65M60 65M06 65N30 65M75 65M12 26A33 35R11 35R07 35R10 PDFBibTeX XMLCite \textit{M. Abbaszadeh} and \textit{M. Dehghan}, Appl. Numer. Math. 169, 44--63 (2021; Zbl 1486.65157) Full Text: DOI
Abbaszadeh, Mostafa; Dehghan, Mehdi The Crank-Nicolson/interpolating stabilized element-free Galerkin method to investigate the fractional Galilei invariant advection-diffusion equation. (English) Zbl 1486.65156 Math. Methods Appl. Sci. 44, No. 4, 2752-2768 (2021). MSC: 65M60 65M06 65N30 65M12 65M15 26A33 35R11 PDFBibTeX XMLCite \textit{M. Abbaszadeh} and \textit{M. Dehghan}, Math. Methods Appl. Sci. 44, No. 4, 2752--2768 (2021; Zbl 1486.65156) Full Text: DOI
Abbaszadeh, Mostafa; Dehghan, Mehdi Numerical investigation of reproducing kernel particle Galerkin method for solving fractional modified distributed-order anomalous sub-diffusion equation with error estimation. (English) Zbl 1474.65340 Appl. Math. Comput. 392, Article ID 125718, 21 p. (2021). MSC: 65M60 34A34 26A33 35R11 65M12 65M75 65M15 PDFBibTeX XMLCite \textit{M. Abbaszadeh} and \textit{M. Dehghan}, Appl. Math. Comput. 392, Article ID 125718, 21 p. (2021; Zbl 1474.65340) Full Text: DOI
Abbaszadeh, Mostafa; Dehghan, Mehdi A POD-based reduced-order Crank-Nicolson/fourth-order alternating direction implicit (ADI) finite difference scheme for solving the two-dimensional distributed-order Riesz space-fractional diffusion equation. (English) Zbl 1452.65145 Appl. Numer. Math. 158, 271-291 (2020). MSC: 65M06 65N06 65M99 65M15 65M12 65D30 35R11 26A33 35K57 PDFBibTeX XMLCite \textit{M. Abbaszadeh} and \textit{M. Dehghan}, Appl. Numer. Math. 158, 271--291 (2020; Zbl 1452.65145) Full Text: DOI
Abbaszadeh, Mostafa; Dehghan, Mehdi; Zhou, Yong Crank-Nicolson/Galerkin spectral method for solving two-dimensional time-space distributed-order weakly singular integro-partial differential equation. (English) Zbl 1435.65170 J. Comput. Appl. Math. 374, Article ID 112739, 16 p. (2020). MSC: 65M70 65M60 65M06 65M12 65M15 35R09 45K05 33C45 26A33 35R11 PDFBibTeX XMLCite \textit{M. Abbaszadeh} et al., J. Comput. Appl. Math. 374, Article ID 112739, 16 p. (2020; Zbl 1435.65170) Full Text: DOI
Assari, Pouria; Dehghan, Mehdi A meshless local Galerkin method for solving Volterra integral equations deduced from nonlinear fractional differential equations using the moving least squares technique. (English) Zbl 1417.65220 Appl. Numer. Math. 143, 276-299 (2019). MSC: 65R20 45D05 26A33 PDFBibTeX XMLCite \textit{P. Assari} and \textit{M. Dehghan}, Appl. Numer. Math. 143, 276--299 (2019; Zbl 1417.65220) Full Text: DOI
Dehghan, Mehdi; Safarpoor, Mansour Application of the dual reciprocity boundary integral equation approach to solve fourth-order time-fractional partial differential equations. (English) Zbl 1499.65709 Int. J. Comput. Math. 95, No. 10, 2066-2081 (2018). MSC: 65N38 35R11 26A33 65D12 65R20 65N80 PDFBibTeX XMLCite \textit{M. Dehghan} and \textit{M. Safarpoor}, Int. J. Comput. Math. 95, No. 10, 2066--2081 (2018; Zbl 1499.65709) Full Text: DOI
Khosravian-Arab, Hassan; Dehghan, Mehdi; Eslahchi, M. R. Generalized Bessel functions: theory and their applications. (English) Zbl 1381.33009 Math. Methods Appl. Sci. 40, No. 18, 6389-6410 (2017). MSC: 33C10 26A33 65D30 65M60 PDFBibTeX XMLCite \textit{H. Khosravian-Arab} et al., Math. Methods Appl. Sci. 40, No. 18, 6389--6410 (2017; Zbl 1381.33009) Full Text: DOI
Dehghan, Mehdi; Abbaszadeh, Mostafa; Deng, Weihua Fourth-order numerical method for the space-time tempered fractional diffusion-wave equation. (English) Zbl 1375.65173 Appl. Math. Lett. 73, 120-127 (2017). MSC: 65R20 26A33 45K05 PDFBibTeX XMLCite \textit{M. Dehghan} et al., Appl. Math. Lett. 73, 120--127 (2017; Zbl 1375.65173) Full Text: DOI
Dehghan, Mehdi; Abbaszadeh, Mostafa Spectral element technique for nonlinear fractional evolution equation, stability and convergence analysis. (English) Zbl 1368.65261 Appl. Numer. Math. 119, 51-66 (2017). MSC: 65R20 45K05 26A33 PDFBibTeX XMLCite \textit{M. Dehghan} and \textit{M. Abbaszadeh}, Appl. Numer. Math. 119, 51--66 (2017; Zbl 1368.65261) Full Text: DOI
Dehghan, Mehdi; Hamedi, Ehsan-Allah; Khosravian-Arab, Hassan A numerical scheme for the solution of a class of fractional variational and optimal control problems using the modified Jacobi polynomials. (English) Zbl 1365.26005 J. Vib. Control 22, No. 6, 1547-1559 (2016). MSC: 26A33 49K21 33C45 PDFBibTeX XMLCite \textit{M. Dehghan} et al., J. Vib. Control 22, No. 6, 1547--1559 (2016; Zbl 1365.26005) Full Text: DOI
Parvizi, M.; Eslahchi, M. R.; Dehghan, Mehdi Numerical solution of fractional advection-diffusion equation with a nonlinear source term. (English) Zbl 1319.35290 Numer. Algorithms 68, No. 3, 601-629 (2015). Reviewer: Răzvan Răducanu (Iaşi) MSC: 35R11 26A33 33C45 65L60 65M70 PDFBibTeX XMLCite \textit{M. Parvizi} et al., Numer. Algorithms 68, No. 3, 601--629 (2015; Zbl 1319.35290) Full Text: DOI
Lotfi, A.; Yousefi, S. A.; Dehghan, Mehdi Numerical solution of a class of fractional optimal control problems via the Legendre orthonormal basis combined with the operational matrix and the Gauss quadrature rule. (English) Zbl 1286.49030 J. Comput. Appl. Math. 250, 143-160 (2013). MSC: 49M30 26A33 PDFBibTeX XMLCite \textit{A. Lotfi} et al., J. Comput. Appl. Math. 250, 143--160 (2013; Zbl 1286.49030) Full Text: DOI
Lakestani, Mehrdad; Dehghan, Mehdi; Irandoust-Pakchin, Safar The construction of operational matrix of fractional derivatives using B-spline functions. (English) Zbl 1276.65015 Commun. Nonlinear Sci. Numer. Simul. 17, No. 3, 1149-1162 (2012). MSC: 65D25 65D07 35R11 65M99 26A33 34K37 34A08 PDFBibTeX XMLCite \textit{M. Lakestani} et al., Commun. Nonlinear Sci. Numer. Simul. 17, No. 3, 1149--1162 (2012; Zbl 1276.65015) Full Text: DOI
Yousefi, S. A.; Lotfi, A.; Dehghan, M. The use of a Legendre multiwavelet collocation method for solving the fractional optimal control problems. (English) Zbl 1271.65105 J. Vib. Control 17, No. 13, 2059-2065 (2011). MSC: 65K10 26A33 PDFBibTeX XMLCite \textit{S. A. Yousefi} et al., J. Vib. Control 17, No. 13, 2059--2065 (2011; Zbl 1271.65105) Full Text: DOI
Saadatmandi, Abbas; Dehghan, Mehdi A Legendre collocation method for fractional integro-differential equations. (English) Zbl 1271.65157 J. Vib. Control 17, No. 13, 2050-2058 (2011). MSC: 65R20 26A33 PDFBibTeX XMLCite \textit{A. Saadatmandi} and \textit{M. Dehghan}, J. Vib. Control 17, No. 13, 2050--2058 (2011; Zbl 1271.65157) Full Text: DOI
Lotfi, A.; Dehghan, Mehdi; Yousefi, S. A. A numerical technique for solving fractional optimal control problems. (English) Zbl 1228.65109 Comput. Math. Appl. 62, No. 3, 1055-1067 (2011). MSC: 65L05 49M30 34A08 26A33 45J05 49K21 PDFBibTeX XMLCite \textit{A. Lotfi} et al., Comput. Math. Appl. 62, No. 3, 1055--1067 (2011; Zbl 1228.65109) Full Text: DOI
Yousefi, S. A.; Dehghan, Mehdi; Lotfi, A. Generalized Euler-Lagrange equations for fractional variational problems with free boundary conditions. (English) Zbl 1228.49016 Comput. Math. Appl. 62, No. 3, 987-995 (2011). MSC: 49K05 26A33 45J05 PDFBibTeX XMLCite \textit{S. A. Yousefi} et al., Comput. Math. Appl. 62, No. 3, 987--995 (2011; Zbl 1228.49016) Full Text: DOI
Saadatmandi, Abbas; Dehghan, Mehdi A new operational matrix for solving fractional-order differential equations. (English) Zbl 1189.65151 Comput. Math. Appl. 59, No. 3, 1326-1336 (2010). MSC: 65L60 26A33 34A08 45J05 PDFBibTeX XMLCite \textit{A. Saadatmandi} and \textit{M. Dehghan}, Comput. Math. Appl. 59, No. 3, 1326--1336 (2010; Zbl 1189.65151) Full Text: DOI
Jafari, Hossein; Dehghan, Mehdi; Sayevand, Khosro Solving a fourth-order fractional diffusion-wave equation in a bounded domain by decomposition method. (English) Zbl 1145.65115 Numer. Methods Partial Differ. Equations 24, No. 4, 1115-1126 (2008). MSC: 65R20 45K05 26A33 PDFBibTeX XMLCite \textit{H. Jafari} et al., Numer. Methods Partial Differ. Equations 24, No. 4, 1115--1126 (2008; Zbl 1145.65115) Full Text: DOI