The Approximate Solutions of Fractional Integro-Differential Equations by Using Modified Adomian Decomposition Method

Document Type : Original Article

Authors

Ahmed Abdullah Hamoud ¹

Kirtiwant Ghadle ²

Shakir Atshan ³

¹ Department of Mathematics Faculty of Education and Science, Taiz University, Taiz, Yemen.

² Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad 431-004, India.

³ Department of Mathematics, Thi Qar Directorates of Education, Ministry of Education, Iraq.

10.22034/kjm.2018.73593

Abstract

The main object of the present paper is to study the behavior of the approximated solutions of the Caputo fractional Volterra-Fredholm integro-differential equations by using modified Adomian decomposition method. Moreover, we discuss some new existence, uniqueness, and convergence results. Finally, an example is included to demonstrate the validity and applicability of the proposed technique.

Keywords

Modified Adomian decomposition method

Caputo fractional derivative

fractional Volterra--Fredholm integro-differential equation

approximate solution

Subjects

• 26 Real functions
• 45 Integral equations
• 49 Calculus of variations and optimal control; optimization

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