Mahgoub Transform Method for Solving Linear Fractional Differential Equations

A. Emimal Kanaga Puhpam; S. Katrin Lydia

doi:https://doi.org/10.14445/22315373/IJMTT-V58P535

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 58 | Number 4 | Year 2018 | Article Id. IJMTT-V58P535 | DOI : https://doi.org/10.14445/22315373/IJMTT-V58P535

Mahgoub Transform Method for Solving Linear Fractional Differential Equations

A. Emimal Kanaga Puhpam, S. Katrin Lydia

Abstract

In this paper, Mahgoub Transform Method has been introduced for solving linear Fractional Differential Equations (FDEs) with constant coefficients. The fractional derivatives are described in the Caputo sense. Some fundamental properties of Mahgoub Transform necessary in solving FDE are derived. The efficiency of this method has been demonstrated using examples.

Keywords

Mahgoub transform, Fractional Differential Equations, Mittag-Leffler.

References

[1] K.Diethelm, The analysis of fractional differential equations: An application-oriented exposition using differential operators of Caputo type,Springer, 2010.
[2] S.Kazem, “Exact Solution of Some Linear Fractional Differential Equations by Laplace Transform”, International Journal of Nonlinear Science,vol. 16, pp. 3-11, 2013.
[3] S.Butera and M. D. Paola,“Fractional differential equations solved by using Mellin transform”. Communications in Nonlinear Science and Numerical Simulation,vol. 19, pp.2220-2227, 2014.
[4] A.Kilbas, Yu. F.Luchko, H. MartinezandJ. J. Trujillo,“Fractional Fourier transform in the framework of fractional calculus operators”, Integral Transforms and Special Functions, vol. 21, pp. 779-795, 2010.
[5] D.S.BodkheandS. K. Panchal,“On Sumudu Transform of fractional derivatives and its applications to Fractional Differential Equations”,Asian Journal of Mathematics and Computer Research, vol. 11, 69-77, 2016.
[6] K.Shahand and R. A. Khan, “The Applications of Natural Transform to the Analytical Solutions of Some Fractional Order Ordinary Differential Equations”,SindhUniversityResearchJournal, vol. 47, 683-686, 2015.
[7] Mohamed and A. E. Elsayed, “Elzaki Transformation for Linear Fractional Differential Equations”,Journal of Computational and Theoretical Nanoscience,vol. 12, pp. 2303-2305, 2015.
[8] R.Khandelwal, P. Choudhary and Y. Khandelwal, “Solution of fractional ordinary differential equation by Kamal transform”, International Journal of Statistics and Applied Mathematics,vol. 3, pp. 279-284, 2018.
[9] K.Diethelm, N. J. Ford and A. D. Freed, “Detailed error analysis for a fractional Adams method”,Numerical Algorithms, vol. 36, pp. 31-52, 2004.
[10] Y.M. Chen, Y. Q. Wei, D. Y. Liu and H. Yu, “Numerical solution for a class of nonlinear variable order fractional differential equations with Legendre wavelets”, Applied Mathematics Letters,vol. 46, pp. 83-88, 2015.
[11] K.Diethelm, N. J. Ford and A. D. Freed, “A predictor–corrector approach for the numerical solution of fractional differential equations”, Nonlinear Dynamics,vol. 29, pp. 3–22, 2002.
[12] M.M. AbdelrahimMahgoub, “The New Integral Transform ''Mahgoub Transform'',Advances in Theoretical and Applied Mathematics,vol. 11, pp. 391-398, 2016.

Citation :

A. Emimal Kanaga Puhpam, S. Katrin Lydia, "Mahgoub Transform Method for Solving Linear Fractional Differential Equations," International Journal of Mathematics Trends and Technology (IJMTT), vol. 58, no. 4, pp. 253-257, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V58P535