A Numerical Method for Solving a Class of Nonlinear Second Order Fractional Volterra Integro-Differntial Type of Singularly Perturbed Problems

Muhammed I. Syam and Mohammed Abu Omar
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Muhammed I. Syam: Department of Mathematical Sciences, College of Science, UAE University, Al-Ain 15551, UAE
Mohammed Abu Omar: Department of Mathematical Sciences, College of Science, UAE University, Al-Ain 15551, UAE

Mathematics, 2018, vol. 6, issue 4, 1-22

Abstract: In this paper, we study a class of fractional nonlinear second order Volterra integro-differential type of singularly perturbed problems with fractional order. We divide the problem into two subproblems. The first subproblems is the reduced problem when ? = 0 . The second subproblems is fractional Volterra integro-differential problem. We use the finite difference method to solve the first problem and the reproducing kernel method to solve the second problem. In addition, we use the pade’ approximation. The results show that the proposed analytical method can achieve excellent results in predicting the solutions of such problems. Theoretical results are presented. Numerical results are presented to show the efficiency of the proposed method.

Keywords: singularly perturbed volterra integro-differntial; caputo fractional derivative; nonlinear boundary value problem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2018
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