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

Author

Listed:
  • 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)

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 ϵ = 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.

Suggested Citation

  • Muhammed I. Syam & Mohammed Abu Omar, 2018. "A Numerical Method for Solving a Class of Nonlinear Second Order Fractional Volterra Integro-Differntial Type of Singularly Perturbed Problems," Mathematics, MDPI, vol. 6(4), pages 1-22, March.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:4:p:48-:d:138192
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    References listed on IDEAS

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    1. Kashkari, Bothayna S.H. & Syam, Muhammed I., 2016. "Fractional-order Legendre operational matrix of fractional integration for solving the Riccati equation with fractional order," Applied Mathematics and Computation, Elsevier, vol. 290(C), pages 281-291.
    2. Sahu, P.K. & Ray, S.Saha, 2015. "Legendre wavelets operational method for the numerical solutions of nonlinear Volterra integro-differential equations system," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 715-723.
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