Generalized Monotone Iterative Method for Caputo Fractional Integro-differential Equation

Authors

  • J. Vasundhara Devi Associate Director, GVP-Prof. Lakshmikantham Institute for Advanced Studies, Professor, Department Of Mathematics, GVP College of Engineering (A), Madhurawada, Visakhapatnam.
  • Chaduvula Venkata Sreedhar Ch v sreedhar, Assistant professor, Department Of Mathematics, GVP College of Engineering (A), Madhurawada, Visakhapatnam

Keywords:

Caputo fractional integro-differential equation, linear integro-differential equations

Abstract

Using coupled lower and upper mathematical solutions we develop the generalized monotone iterative technique to solve Caputo fractional integro-differential equation of order q with periodic boundary condition, via initial value problem (IVP) where $0<q<1.$ We construct monotone iterates which are solutions of initial value problems associated with linear integro-differential equations, that are easier to obtain. In fact, we have obtained the explicit mathematical solution of the linear IVP of Caputo fractional integro-differential equation. We show that these iterates converge uniformly and monotonically to coupled minimal and maximal solutions of the problem considered here.

Author Biographies

  • J. Vasundhara Devi, Associate Director, GVP-Prof. Lakshmikantham Institute for Advanced Studies, Professor, Department Of Mathematics, GVP College of Engineering (A), Madhurawada, Visakhapatnam.
    Professor, Department Of Mathematics
  • Chaduvula Venkata Sreedhar, Ch v sreedhar, Assistant professor, Department Of Mathematics, GVP College of Engineering (A), Madhurawada, Visakhapatnam
    Assistant Professor, Department of Mathemaitcs.

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Published

2016-10-30

Issue

Vol. 9 No. 4: (October 2016)

Section

Differential Equations

License

Upon acceptance of an article by the journal, the author(s) accept(s) the transfer of copyright of the article to European Journal of Pure and Applied Mathematics.

European Journal of Pure and Applied Mathematics will be Copyright Holder.

How to Cite

Generalized Monotone Iterative Method for Caputo Fractional Integro-differential Equation. (2016). European Journal of Pure and Applied Mathematics, 9(4), 346-359. https://ejpam.com/index.php/ejpam/article/view/2714