Existence and uniqueness of solutions for multi-term nonlinear fractional integro-differential equations

Dumitru Baleanu,Sayyedeh Zahra Nazemi,Shahram Rezapour

doi:10.1186/1687-1847-2013-368

Abstract

In this manuscript, by using the fixed point theorems, the existence and the uniqueness of solutions for multi-term nonlinear fractional integro-differential equations are reported. Two examples are presented to illustrate our results.

Highlights

1 Introduction The study of fractional differential equations ranges from the theoretical aspects of existence and uniqueness of solutions to the analytic and numerical methods for finding solutions
In, Xinwei and Landong reviewed the existence of solutions for the nonlinear fractional differential equation cDαu(t) = f t, u(t), cDβ u(t) ( < t < )
In, Ahmad and Sivasundaram studied the existence of solutions for the nonlinear fractional integro-differential equation cDqu(t) = f t, u(t),(t),(t) ( < t < and < q ≤ )

Summary

Introduction

The study of fractional differential equations ranges from the theoretical aspects of existence and uniqueness of solutions to the analytic and numerical methods for finding solutions. In , Xinwei and Landong reviewed the existence of solutions for the nonlinear fractional differential equation cDαu(t) = f t, u(t), cDβ u(t) ( < t < )

Results

Conclusion