Solution of Multi-order Fractional Differential Equation Based on Conformable Derivative by Shifted Legendre Polynomial

Keywords: conformable derivative, fractional derivative, shifted Legendre polynomial, fractional deferential equation, python program


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.


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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.

How to Cite
Mahmood S, Hamad K, kareem‎, Shex A. Solution of Multi-order Fractional Differential Equation Based on Conformable Derivative by Shifted Legendre Polynomial. cuesj [Internet]. 20Dec.2021 [cited 16Apr.2024];5(2):64-8. Available from:
Research Article