Application of the Aboodh Transform for Solving Fractional Delay Differential Equations

Year 2020, , 93 - 101, 29.09.2020

Mohamed Elarbı Benattıa , Kacem Belghaba

https://doi.org/10.32323/ujma.702033

Cited By: 20

Abstract

In this article, we extend the concept of the Aboodh transform to the solution of partial differential equations of fractional order using Caputo's fractional derivative. The transformation concerned is applicable to solve many classes of partial differential equations with derivatives of order and integrals. Consequently, the fractional Delay Differential Equations (DDEs) which we are going to study in this work. The resulting numerical proofs show that the method converges favorably towards the analytical solution.

Keywords

Aboodh Transform, Fractional Delay differential Equation, Partial derivatives

References

• [1] M. Elarbi Benattia, K. Belghaba, Application of the Galerkin method with Chebyshev polynomials for solving the integral equation, J. Comput. Sci. Comp. Math., DOI: 10.20967/jcscm.2017.03.008.
• [2] M. Elarbi Benattia, K. Belghaba, The analytical solution Of Telegraph equation Of space-fractional order derivative by the Aboodh transform Method, Int. J. Anal. Appl., 18(2), (2020), 243-253.
• [3] Ebimene, J. Mamadu, Ignatius N. Njoseh, Solving delay differential equationns by Elzaki transform method, Boson J. Modern Phys., (BJMP)3-1 (2017).
• [4] H. Eltayeb, E. Abdeldaiem, Sumudu decomposition method for solving fractional delay differential equations, Res. Appl. Math,, 1 (2017), 1-13.
• [5] F. Ismail, R.A. Al-Khasawneh, A.S. Lwin and M. Suleiman, Numerical treatment of delay differential equations by Runge-Kutta method using hermite interpolation, Matematika, 18(2), (2002), 79–90.
• [6] S.T. Demiray, H. Bulut and F.B.M. Belgacem, Sumudu transform method for analytical solutions of fractional type ordinary differential equations, J. Math. Prob. Eng., (2015). http://dx.doi.org/10.1155/2014/131690.
• [7] H. Smith, An Introduction to Delay Differential Equations with Applications to the Life Sciences, Springer, New York, NY, USA, 2011.
• [8] S.T. Mohyud-Dina and A. Yıldırım, Variational iteration method for delay differential equations using He’s polynomials, Z. Naturforsch. 65a (2010), 1045–1048.
• [9] Abas.I. Khlaif. Approximate solutions for delay differential equations of fractional order. Thesis(B.Sc mathematics/ College science/ Al -Nahrain university 2012).