# 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.

2016-10-30

## How to Cite

Devi, J. V., & Sreedhar, C. V. (2016). Generalized Monotone Iterative Method for Caputo Fractional Integro-differential Equation. European Journal of Pure and Applied Mathematics, 9(4), 346–359. Retrieved from https://www.ejpam.com/index.php/ejpam/article/view/2714

## Section

Differential Equations