Solutions of nonlinear fractional integro - differential equations by combined sumudu transform with adomian decomposition approach

Hussein, Qays Jasem; Altaie, Huda Omran

doi:10.47974/JIM-1592

Open Access Research Article

Solutions of nonlinear fractional integro - differential equations by combined sumudu transform with adomian decomposition approach

^*Qays Jasem HusseinCorresponding authorqaisalsaadm@gmail.comDepartment of Mathematics College of Education For Pure Sciences (Ibn Al-Haitham) University of Baghdad Department of Mathematics College of Education for Pure Sciences (Ibn Al-Haitham) University of BaghdadBaghdad, IraqView full profile → , Huda Omran Altaiehuda.h.o@ihcoedu.uobaghdad.edu.iqDepartment of Mathematics College of Education For Pure Sciences (Ibn Al-Haitham) University of Baghdad Department of Mathematics College of Education for Pure Science (Ibn Al-Haitham) University of Baghdad Baghdad, 10071, IraqView full profile →

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pp. 1665–1670Vol. 26Issue 7October 2023DOI: 10.47974/JIM-1592XML

Published Online:: 01 Nov 2023
Article type:: Research Article
Language:: EN
Article no.:: JIM-1592
Pages:: 1665–1670

Abstract

The Caputo formulation is used to handle fractional derivatives in this study. The well-known method form employs Adomian’s polynomials as the proper mathematical tool for dealing with nonlinear variables. The integral equation may be solved by applying the Sumudu transformation to both sides and then the terms can be written out. The solution is given as a convergent infinite series. Nonlinear Volterra integro-differential equations with fractional derivatives are amenable to the proposed method. The results strongly support the validity, applicability, and efficacy of the approach.

Keywords

A duopoly economy Market share Mathematical modeling Ordinary differential equations

Subject Classifications

05C7211J54

References

[1] Watuagala, G.K. Sumudu transform: An integral transform to solve differential equation and control engineering problems. Int. J.Math. Educ. Sci. Technol. 24, 35–42 (1993).
[2] Katatbeh, Q.D.; Belgacem, F.B.M. Applications of the Sumudu transform to fractional differential equations. Nonlin. Stud. (2011).
[3] Abdolamir, K.; Mohammad, M.M.; Hamed, H.M. Exact Solution of Time-Fractional Partial Differential Equations Using SumuduTransform. WSEAS Trans. Math. (2014).
[4] Ahmed A.; Kirtiwant, P.G.; Shakir, M.A. The approximate solutions of fractional integro-differential equations by using modified Adomian decomposition method. Khayyam J. Math. (2019).
[5] Saadatmandi, A.; Dehghan, M. A Legendre collocation method for fractional integro-differential equations. J. Vib. Control (2011).
[6] HH Omran, Solutins of Systems for the Linear Fredholm-Volterra Integral Equations of the Second Kind, Ibn AL-Haitham Journal For Pure and Applied Science, 017, 23, 2, 200-206.
[7] Maad G.M and Huda Omran Altaie, Study on Approximate Analytical Methods For Nonlinear Differential Equations, Journal of Interdiscplinary Mathematics,Vol 25, Issue 8 (2022).
[8] Maad G.M and Huda Omran Altaie, Efficient Analytical Method For The Solution of Some Fractional -Order Nonlinear Differential Equations, International Journal of Nonlinear Analysis and Applications (July 2022).
[9] Maad G.M and Huda Omran Altaie, A new Technique for Solving Fractional Nonlinear Equations by Sumudu Transform and Adomian Decomposition Method, Ibn Al-Haitham Journal for Pure and Applied sciences (20 july 2022).
[10] Huda Omran Altaie, Two Efficient Methods For Solving Nonlinear Fourth-Order PDEs, International Journal of Nonlinear Analysis and Applications, Volume 11, 543-546 (2020).
[11] Fadhel S.Fadhel, Huda Omran Altaie, Solution of Riccati Matrix Differential Equation Using New Approach of Variational Iteration Method, Int. J. Nonlinear Anal. Appl. 12 (2021).
[12] Huda Omran Altaie, Comparison the solutions for some kinds of differential equations using iterative methods, Journal of Interdisciplinary Mathematics 24 (5), 1113-1118.
[13] Luma Naji Mohammed Tawfiq and Huda Altaie Recent Modification of Homotopy Perturbation Method for Solving System of Third Order PDEs, Journal of Physics: Conference Series 1530 (1) (2020).
[14] Altaie, H.O. Study the Stability for Ordinary Differential Equations Using New Techniques via Numerical Methods, Advances in Intelligent Systems and Computing, 1292, pp. 509–516 (2021).
[15] Hassan, M. M. : Topological Mappings Based on SPG*-Closed. Wasit Journal of Computer and Mathematics Science, 1(3) (2022).‏

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