References
- Ahmed E, Elgazzar A. On fractional order differential equations model for nonlocal epidemics. Phys A: Stat Mech Appl. 2007;379(2):607–614. doi: 10.1016/j.physa.2007.01.010
- Sun H, Chen D, Zhang Y, et al. Understanding partial bed-load transport: experiments and stochastic model analysis. J Hydrol. 2015;521:196–204. doi: 10.1016/j.jhydrol.2014.11.064
- Sun H, Chen W, Chen Y. Variable-order fractional differential operators in anomalous diffusion modeling. Phys A: Stat Mech Appl. 2009;388(21):4586–4592. doi: 10.1016/j.physa.2009.07.024
- Zabidi NA, Abdul Majid Z, Kilicman A, et al. Numerical solutions of fractional differential equations by using fractional explicit adams method. Mathematics. 2020;8(10):1675. doi: 10.3390/math8101675
- Vargas AM. Finite difference method for solving fractional differential equations at irregular meshes. Math Comput Simul. 2022;193:204–216. doi: 10.1016/j.matcom.2021.10.010
- Min C, Chen Y. Semi-classical jacobi polynomials, hankel determinants and asymptotics. Anal Math Phys. 2022;12:1–25. doi: 10.1007/s13324-021-00619-9
- Rai N, Mondal S. Spectral methods to solve nonlinear problems: A review. Partial Differ Equ Appl Math. 2021;4:100–143.
- Doha EH, Bhrawy AH, Ezz-Eldien SS. A chebyshev spectral method based on operational matrix for initial and boundary value problems of fractional order. Comput Math Appl. 2011;62(5):2364–2373. doi: 10.1016/j.camwa.2011.07.024
- Bhrawy A, Zaky M. A fractional-order jacobi tau method for a class of time-fractional pdes with variable coefficients. Math Methods Appl Sci. 2016;39(7):1765–1779. doi: 10.1002/mma.v39.7
- Zaky MA. A legendre spectral quadrature tau method for the multi-term time-fractional diffusion equations. Comput Appl Math. 2018;37(3):3525–3538. doi: 10.1007/s40314-017-0530-1
- Zaky MA. An improved tau method for the multi-dimensional fractional rayleigh–stokes problem for a heated generalized second grade fluid. Comput Math Appl. 2018;75(7):2243–2258. doi: 10.1016/j.camwa.2017.12.004
- Bhrawy AH, Taha TM. An operational matrix of fractional integration of the laguerre polynomials and its application on a semi-infinite interval. Math Sci. 2012;6(1):41. doi: 10.1186/2251-7456-6-41
- Kazem S. An integral operational matrix based on jacobi polynomials for solving fractional-order differential equations. Appl Math Model. 2013;37(3):1126–1136. doi: 10.1016/j.apm.2012.03.033
- Al-Sharif M, Ahmed A, Salim M. An integral operational matrix of fractional-order chelyshkov functions and its applications. Symmetry. 2020;12(11):1755. doi: 10.3390/sym12111755
- Saadatmandi A, Dehghan M. A new operational matrix for solving fractional-order differential equations. Comput Math Appl. 2010;59(3):1326–1336. doi: 10.1016/j.camwa.2009.07.006
- Bhrawy A, Baleanu D, Assas L, et al. On a generalized laguerre operational matrix of fractional integration. Math Problems Eng. 2013;2013:1–7. doi: 10.1155/2013/569286
- Baleanu D, Bhrawy A, Taha T. A modified generalized laguerre spectral method for fractional differential equations on the half line. Abstr Appl Anal. 2013;2013:1–12.
- Podlubny I. Fractional differential equations. San Diego (CA): Academic Press, Inc.; 1999. p. 340. (Mathematics in science and engineering; vol. 198). An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications.
- Raja MAZ, Khan JA, Qureshi IM. Solution of fractional order system of bagley-torvik equation using evolutionary computational intelligence. Math Problems Eng. 2011;2011:1–18. doi: 10.1155/2011/675075
- Raja MAZ, Khan JA, Qureshi IM. Swarm intelligence optimized neural networks in solving fractional system of bagley-torvik equation. Intell Syst Eng. 2011;19(1):41–51.
- Raja MAZ, Samar R, Manzar MA, et al. Design of unsupervised fractional neural network model optimized with interior point algorithm for solving bagley–torvik equation. Math Comput Simul. 2017;132:139–158. doi: 10.1016/j.matcom.2016.08.002
- Verma A, Kumar M. Numerical solution of bagley–torvik equations using legendre artificial neural network method. Evol Intell. 2021;14:2027–2037. doi: 10.1007/s12065-020-00481-x
- Ghorbani A, Alavi A. Application of he's variational iteration method to solve semidifferential equations of nth order. Math Problems Eng. 2008;2008:1–9. doi: 10.1155/2008/627983
- Miller KS, Ross B. An introduction to the fractional calculus and fractional differential equations. New York: Wiley; 1993.
- Spanier J, Oldham K. The laguerre polynomials ln(x). ch. 23 in an Atlas of functions. New York, NY: Springer, 1987. p. 209–216. doi:10.1007/978-0-387-48807-3_24
- Arfken G. Laguerre functions. USA: Academic Press Orlando; 1985.
- Andrews G, Askey R, Roy R. Laguerre polynomials. UK: Cambridge University Press; 1999. p. 282–293.
- Laguerre E. Sur la transformation des fonctions elliptiques. Bull Soc Math. 1878;6:72–78.
- Litko JR. Gi/g/1 interdeparture time and queue-length distributions via the laguerre transform. Queueing Syst. 1989;4:367–381. doi: 10.1007/BF01159474
- Sumita U. Development of the laguerre transform method for numerical exploration of applied probability models [Ph.D. dissertation]. Rochester (NY): Graduate School of Management, University of Rochester; 1982.
- Keilson J, Sumita U. Waiting time distribution response to traffic surges via the Laguerre transform. New York: Springer; 1982.
- Schatz GC, Ratner MA. Quantum mechanics in chemistry. UK: Courier Corporation; 2002.
- Merzbacher E. Quantum mechanics. New York: John Wiley & Sons; 1998.
- Baykal M, Baykal A. Laguerre polynomials by a harmonic oscillator. Eur J Phys. 2014;35(5):055005. doi: 10.1088/0143-0807/35/5/055005
- Doha E, Youssri Y. On the connection coefficients and recurrence relations arising from expansions in series of modified generalized laguerre polynomials: applications on a semi-infinite domain. Nonlinear Eng. 2019;8(1):318–327. doi: 10.1515/nleng-2018-0073
- Bassuony M, Abd-Elhameed W, Doha E, et al. A legendre-laguerre-galerkin method for uniform euler-bernoulli beam equation. East Asian J Appl Math. 2018;8(2):280–295. doi: 10.4208/eajam
- Bhrawy AH, Alhamed YA, Baleanu D, et al. New spectral techniques for systems of fractional differential equations using fractional-order generalized laguerre orthogonal functions. Fract Calc Appl Anal. 2014;17:1137–1157. doi: 10.2478/s13540-014-0218-9
- Youssri YH. A new operational matrix of caputo fractional derivatives of fermat polynomials: an application for solving the bagley-torvik equation. Adv Differ Equ. 2017;2017:1–17. doi: 10.1186/s13662-017-1123-4
- Torvik PJ, Bagley RL. On the appearance of the fractional derivative in the behavior of real materials. J Appl Mech. 1984;51:294–298. doi: 10.1115/1.3167615