Solution of Multi-order Fractional Differential Equation Based on Conformable Derivative by Shifted Legendre Polynomial
The aim of this article is the way for finding approximation solution of multi-order fractional differential equation with conformable sense with use approximated function by shifted Legendre polynomial, the method is easy and powerful for get our results of the linear and non-linear equation, the background idea behind this method is finding system of algebra after achieving messing variable is that mean obtain approximate solution, a few examples illustrates for presented how much our method is capable.
M. Abul-Ez, M. Zayed, A. Youssef and M. De la Sen. On conformable fractional Legendre polynomials and their convergence properties with applications. Alexandria Engineering Journal, vol. 59, no. 6, pp. 5231-5245, 2020.
H. Çerdik Yaslan and F. Mutlu. Numerical solution of the conformable differential equations via shifted Legendre polynomials. International Journal of Computer Mathematics, vol. 97, no.5, pp. 1016-1028, 2020.
E. Hesameddini and E. Asadollahifar. Numerical solution of multi-order fractional differential equation. IJNAO, vol. 5, no. 1, pp. 37-48, 2015.
S. S. Ezz-Eldien, J. A. Machado, Y. Wang and A. A. Aldraiweesh. An algorithm for the approximate solution of the fractional Riccati differential equation. International Journal of Nonlinear Sciences and Numerical Simulation, vol. 20, no. 6, pp. 661-674, 2019.
H. Khalil, R. H. Ali Khan, M. A Al-Smadi, A. Freihat and N. Shawagfeh. New operational matrix for shifted legendre polynomials. Punjab University Journal of Mathematics, vol. 47, no. 1, pp. 1-23, 2020.
M. M. Khader, T. S. El Danaf and A. S. Hendy. Efficient spectral collocation method for solving multi-term fractional differential equations based on the generalized Laguerre polynomials. J. Fractional Calc. Appl, vol. 3, pp. 1-14, 2012.
R. A. Khalil. A new definition of fractional derivative. Journal of Computational and Applied Mathematics, vol. 264, pp. 65-70, 2014.
A. B. Kisabo, U. C. Uchenna, and F. A. Adebimpe. Newton’s method for solving non-linear system of algebraic equations (NLSAEs) with MATLAB/Simulink® and MAPLE®. American Journal of Mathematical and Computer Modelling, vol. 2, no. 4, pp. 117-131, 2017.
L. Yuanlu. Solving a nonlinear fractional differential equation using Chebyshev wavelets. Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 9, pp. 2284-2292, 2010.
Copyright (c) 2021 Salim S. Mahmood, Kamaran J. Hamad, Milad A. kareem, Asrin F. Shex
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Authors who publish with this journal agree to the following terms:
1. Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License [CC BY-NC-ND 4.0] that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
2. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
3. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).