[1] P. Agarwal, D. Baleanu, Y. Chen, S. Momani and J. A. T. Machado, Fractional Calculus, In ICFDA: International Workshop on Advanced Theory and Applications of Fractional Calculus, Amman, 2018.
[2] S. Salahshour, A. Ahmadian, N. Senu, D. Baleanu and P. Agarwal, On analytical solutions of the fractional differential equation with uncertainty: application to the basset problem, Entropy 17 (2015) 885–902, https://doi.org/10.3390/e17020885.
[3] P. Agarwal and J. Choi, Fractional calculus operators and their image formulas, J. Korean Math. Soc. 53 (2016) 1183–1210, https://doi.org/10.4134/JKMS.j150458.
[4] R. Akbari and L. Navaei, Fractional dynamics of infectious disease transmission with optimal control, Math. Interdisc. Res. 9 (2024) 199–213, https://doi.org/10.22052/MIR.2023.253000.1410.
[5] M. Valizadeh, Y. Mahmoudi and F. Dastmalchi Saei, On fractional linear multi-step methods for fractional order multi-delay nonlinear pantograph equation, Comput. Methods Differ. Equ. 12 (2024) 511–522, https://doi.org/10.22034/cmde.2023.58018.2444.
[6] M. Pourbabaee and A. Saadatmandi, A new operational matrix based on Müntz-Legendre polynomials for solving distributed order fractional differential equations, Math. Comput. Simulation 194 (2022) 210–235, https://doi.org/10.1016/j.matcom.2021.11.023.
[7] M. Bisheh-Niasar, The effect of the Caputo fractional derivative on polynomiography, Math. Interdisc. Res. 8 (2023) 347–358,
https://doi.org/10.22052/MIR.2022.246736.1367.
[8] Z. Hammouch, T. Mekkaoui and P. Agarwal, Optical solitons for the Calogero-Bogoyavlenskii-Schiff equation in (2 + 1) dimensions with time-fractional conformable derivative, Eur. Phys. J. Plus 133 (2018) 1–6, https://doi.org/10.1140/epjp/i2018-12096-8.
[9] N. A. Shah, P. Agarwal, J. D. Chung, S. Althobaiti, S. Sayed, A. F. Aljohani and M. Alkafafy, Analysis of time-fractional Burgers and diffusion equations by using modified q-HATM, Fractals 30 (2022) #2240012, https://doi.org/10.1142/S0218348X22400126.
[10] L. Shi, S. Rashid, S. Sultana, A. Khalid, P. Agarwal and M. S. Osman, Semianalytical view of time-fractional PDES with proportional delays pertaining to index and Mittag-Leffler memory interacting with hybrid transforms, Fractals 31 (2023) #2340071, https://doi.org/10.1142/S0218348X23400716.
[11] A. Saadatmandi, M. Dehghan and M. R. Azizi, The Sinc-Legendre collocation method for a class of fractional convection-diffusion equations with variable coefficients, Commun. Nonlinear Sci. Numer. Simul. 17 (2012) 4125–4136,
https://doi.org/10.1016/j.cnsns.2012.03.003.
[12] S. Sabermahani, Y. Ordokhani and S. A. Yousefi, Fractional-order general Lagrange scaling functions and their applications, Bit Numer. Math. 60 (2020) 101–128, https://doi.org/10.1007/s10543-019-00769-0.
[13] A. S. Hendy and M. A. Zaky, A priori estimates to solutions of the time-fractional convection-diffusion-reaction equation coupled with the Darcy system, Commun. Nonlinear Sci. Numer. Simul. 109 (2022) #106288, https://doi.org/10.1016/j.cnsns.2022.106288.
[14] L. Sun, X. Yan and T. Wei, Identification of time-dependent convection coefficient in a time-fractional diffusion equation, J. Comput. Appl. Math. 346 (2019) 505–517, https://doi.org/10.1016/j.cam.2018.07.029.
[15] R. Kamal Kamran, G. Rahmat and K. Shah, On the numerical approximation of three-dimensional time fractional convection-diffusion equations, Math. Probl. Eng. 2021 (2021) #4640467, https://doi.org/10.1155/2021/4640467.
[16] L. J. Chen, M. Li and Q. Xu, Sinc-galerkin method for solving the time fractional convection-diffusion equation with variable coefficients, Adv. Differ. Equ. 504 (2020) #504, https://doi.org/10.1186/s13662-020-02959-5.
[17] A. Chang, H. Sun, C. Zheng, B. Lu, C. Lu, R. Ma, Y. Zhang, A time fractional convection-diffusion equation to model gas transport through heterogeneous soil and gas reservoirs, Phys. A: Stat. Mech. Appl. 502 (2018) 356–369,
https://doi.org/10.1016/j.physa.2018.02.080.
[18] M. R. S. Ammi and I. Jamiai, Finite difference and Legendre spectral method for a timefractional diffusion-convection equation for image restoration, Discrete Contin. Dyn. Syst. Ser. S 11 (2018) 103–117, https://doi.org/10.3934/dcdss.2018007.
[19] X. Wang, D. Posny and J. Wang, A reaction-convection-diffusion model for cholera spatial dynamics, Discrete Contin. Dyn. Syst. Ser. B 21 (2016) 2785–2809,
https://doi.org/10.3934/dcdsb.2016073.
[20] S. Nagar, R. C. Korzekwa and K. Korzekwa, Continuous intestinal absorption model based on the convection-diffusion equation, Mol. Pharm. 14 (2017) 3069–3086, https://doi.org/10.1021/acs.molpharmaceut.7b00286.
[21] M. P. D. Comsa, R. Phlypo and P. Grangeat, Inverting the diffusion-convection equation for gas desorption through an homogeneous membrane by Kalman filtering, In 2022 30th European Signal Processing Conference (EUSIPCO) 1318–1322 IEEE (2022).
[22] M. Abbaszadeh, A. Bagheri Salec, S. Kamel and A. Al-Khafaji, The effect of fractional-order derivative for pattern formation of brusselator reaction–diffusion model occurring in chemical reactions, Iranian J. Math. Chem. 14 (2023) 243–269, https://doi.org/10.22052/IJMC.2023.253498.1759.
[23] R. Hilfer, Applications of Fractional Calculus in Physics, World Scientific, Singapore, 2000.
[24] I. M. Sokolov, J. Klafter and A. Blumen, Fractional kinetics, Phys. Today. 55 (2002) 48–54.
[25] R. F. Sincovec and N. K. Madsen, Software for nonlinear partial differential equations, ACM Trans. Math. Softw. 1 (1975) 232–260.
[26] X. Li and C. Xu, Existence and uniqueness of the weak solution of the space-time fractional diffusion equation and a spectral method approximation, Commun. Comput. Phys. 8 (2010) 1016–1051, https://doi.org/10.4208/cicp.020709.221209a.
[27] L. Sun, X. Yan and T. Wei, Identification of time-dependent convection coefficient in a time-fractional diffusion equation, J. Comput. Appl. Math. 346 (2019) 505–517, https://doi.org/10.1016/j.cam.2018.07.029.
[28] F. Liu, P. Zhuang, V. Anh, I. Turner and K. Burrage, Stability and convergence of the difference methods for the space-time fractional advection-diffusion equation, Appl. Math. Comput. 191 (2007) 12–20, https://doi.org/10.1016/j.amc.2006.08.162.
[29] H. Safdari, Y. E. Aghdam and J. F. Gómez-Aguilar, Shifted Chebyshev collocation of the fourth kind with convergence analysis for the space-time fractional advection-diffusion equation, Eng. Comput. 38 (2022) 1409–1420, https://doi.org/10.1007/s00366-020-01092-x.
[30] E. Sokhanvar, A. Askari-Hemmat and S. A. Yousefi, Legendre multiwavelet functions for numerical solution of multi-term time-space convection-diffusion equations of fractional order, Eng. Comput. 37 (2021) 1473–1484, https://doi.org/10.1007/s00366-019-00896-w.
[31] A. Shirzadi, L. Ling and S. Abbasbandy, Meshless simulations of the two-dimensional fractional-time convection-diffusion-reaction equations, Eng. Anal. Bound. Elem. 36 (2012) 1522–1527, https://doi.org/10.1016/j.enganabound.2012.05.005.
[32] M. M. Izadkhah and J. Saberi-Nadjafi, Gegenbauer spectral method for time-fractional convection-diffusion equations with variable coefficients, Math. Methods Appl. Sci. 38 (2015) 3183–3194, https://doi.org/10.1002/mma.3289.
[33] M. Sh. Dahaghin and H. Hassani, A new optimization method for a class of time fractional convection-diffusion-wave equations with variable coefficients, Eur. Phys. J. Plus 132 (2017) 1–13,
https://doi.org/10.1140/epjp/i2017-11407-y.
[34] M. Behroozifar and A. Sazmand, An approximate solution based on Jacobi polynomials for time-fractional convection-diffusion equation, Appl. Math. Comput. 296 (2017) 1–17, https://doi.org/10.1016/j.amc.2016.09.028.
[35] G. T. Lubo and G. F. Duressa, Linear B-spline finite element Method for solving delay reaction diffusion equation, Comput. Methods Differ. Equ. 11 (2023) 161–174, https://doi.org/10.22034/CMDE.2022.49678.2066.
[36] E. Keshavarz, Y. Ordokhani and M. Razzaghi, A numerical solution for fractional optimal control problems via Bernoulli polynomials, J. Vib. Control 22 (2016) 3889–3903, https://doi.org/10.1177/1077546314567181.
[37] S. Sabermahani and Y. Ordokhani, Fibonacci wavelets and Galerkin method to investigate fractional optimal control problems with bibliometric analysis, J. Vib. Control 27 (2021) 1778–1792, https://doi.org/10.1177/1077546320948346.
[38] F. Nourian, M. Lakestani, S. Sabermahani and Y. Ordokhani, Touchard wavelet technique for solving time-fractional Black-Scholes model, Comp. Appl. Math. 41 (2022) 3150, https://doi.org/10.1007/s40314-022-01853-y.
[39] P. T. Toan, T. N. Vo and M. Razzaghi, Taylor wavelet method for fractional delay differential equations, Eng. Comput. 37 (2021) 231–240, https://doi.org/10.1007/s00366-019-00818-w.
[40] Y. Tasyurdu, D. Çifçi and Ö. Deveci, Applications of Pell polynomials in rings, J. Math. Res. 10 (2018) 35–41, https://doi.org/10.5539/jmr.v10n3p35.
[41] M. Taghipour and H. Aminikhah, A fast collocation method for solving the weakly singular fractional integro-differential equation. Computational and Applied Mathematics, Comp. Appl. Math. 41 (2022) 1–38, https://doi.org/10.1007/s40314-022-01845-y.
[42] P. F. Byrd, Expansion of analytic functions in polynomials associated with Fibonacci numbers, Fibonacci Quart. 1 (1963) 16–29.
[43] S. Sabermahani, Y. Ordokhani and M. Razzaghi, Ritz-generalized Pell wavelet method: Application for two classes of fractional pantograph problems, Commun. Nonlinear Sci. Numer. Simul. 119 (2023) #107138, https://doi.org/10.1016/j.cnsns.2023.107138.
[44] S. Mashayekhi and M. Razzaghi, Numerical solution of distributed order fractional differential equations by hybrid functions, J. Comput. Phys. 315 (2016) 169–181, https://doi.org/10.1016/j.jcp.2016.01.041.
[45] S. Sabermahani, Y. Ordokhani and S. A. Yousefi, Fibonacci wavelets and their applications for solving two classes of time-varying delay problems, Optimal Control Appl. Methods 41 (2020) 395–416, https://doi.org/10.1002/oca.2549.
[46] C. Canuto, M. Y. Hussaini, A. Quarteroni and T. A. Zang, Spectral Methods: Fundamentals in Single Domains, Springer-Verlag Berlin Heidelberg, 2006.
[47] H. Dehestani, Y. Ordokhani and M. Razzaghi, On the applicability of Genocchi wavelet method for different kinds of fractional-order differential equations with delay, Numer. Linear Algebra Appl. 26 (2019) #e2259,
https://doi.org/10.1002/nla.2259.
[48] F. Zhou and X. Xu, The third kind Chebyshev wavelets collocation method for solving the time-fractional convection diffusion equations with variable coefficients, Appl. Math. Comput. 280 (2016) 11–29, https://doi.org/10.1016/j.amc.2016.01.029.
[49] Y. Chen, Y. Wu, Y. Cui, Z. Wang and D. Jin, Wavelet method for a class of fractional convection-diffusion equation with variable coefficients. J. Comput. Sci., 1 (2010) 146–149, https://doi.org/10.1016/j.jocs.2010.07.001.
[50] J. Zhang, X. Zhang and B. Yang, An approximation scheme for the time fractional convection-diffusion equation, Appl. Math. Comput. 335 (2018) 305–312, https://doi.org/10.1016/j.amc.2018.04.019.
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