Numerical Solution of Fractional Differential Equations by ADM

Nuha Mohammed Dabwan; Somaia Ali Alaqel; Yahya Qaid Hasan

doi:https://doi.org/10.14445/22315373/IJMTT-V66I11P501

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 66 | Issue 11 | Year 2020 | Article Id. IJMTT-V66I11P501 | DOI : https://doi.org/10.14445/22315373/IJMTT-V66I11P501

Numerical Solution of Fractional Differential Equations by ADM

Nuha Mohammed Dabwan, Somaia Ali Alaqel, Yahya Qaid Hasan

Citation :

Nuha Mohammed Dabwan, Somaia Ali Alaqel, Yahya Qaid Hasan, "Numerical Solution of Fractional Differential Equations by ADM," International Journal of Mathematics Trends and Technology (IJMTT), vol. 66, no. 11, pp. 1-12, 2020. Crossref, https://doi.org/10.14445/22315373/IJMTT-V66I11P501

Abstract

Due to the role played by fractional differential equations in various sciences, many studies have been submitted to study them. In this paper, we focus on finding approximate solutions of fractional differential equations using Adomian Decomposition Method (ADM). In this paper, three numerical examples are solved. These examples showed the ease of finding approximate solutions of these equations using MADM.

Keywords

Fractional Equations, Adomian Method, Boundary Conditions

References

[1] Podlubny I. Fractional Differential Equations, San Diego: Academic- Press, 1999.
[2] Miller K S, Ross B. An Introduction to the Fractional Calculus and Fractional Differential Equations, New York: Wiley, 1993.
[3] Shimizu N, Zhang W. Fractional calculus approach to dynamic problems of viscoelastic materials, JSME Series C{Mechanical Systems, Machine Elements and Manufacturing, 1999, 42: 825-837.
[4] Adomian G. A review of the decomposition method and some recent results for nonlinear equations, Math. Comput. Appl. (1990), 1: 17- 43. 11
[5] Adomian G. A review of the decomposition in applied mathematics, Math. Anal. Appl. (1990), 1: 501-544.
[6] Adomian G. Solving frontier problem of physics: the decomposition method, Kluwer academic publishers London, 1994.
[7] Dabwan N. M, Hasan Y. Q. Solutions of Fractional Differential Equations by Modified Adomian Decomposition Method, Advances in Mathemat- ics: Scientific Journal (2020), 9(7): 4761-4767.
[8] Dabwan N. M, Hasan Y. Q. Using Adomian Decomposition Method in Solving Fractional Lane-Emden Type Equations, Research and Analy- sis Journal, 2020, 3(8): 274-283.
[9] Hasan Y.Q. The numerical solution of third-order boundary value prob- lems by the modified decomposition method, Advances in Intelligent Transportation Systems. 2012, 1(3): 71-74.
[10] Khalil R, Al Horani M, Yousef A, Sababheb M. A new definitions of fractional derivative, Journal of Computational and Applied Mathematics, 2014, 264:65-70.