Existence and uniqueness for a class of iterative fractional differential equations

Rabha W Ibrahim,Faten H Damag,Adem Kılıçman

doi:10.1186/s13662-015-0421-y

Rabha W Ibrahim, Faten H Damag + Show 1 more

Open Access

https://doi.org/10.1186/s13662-015-0421-y

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Abstract

The presence of a self-mapping increases the difficulty in proving the existence and uniqueness of solutions for general iterative fractional differential equations. In this article, we provide conditions for the existence and uniqueness of solutions for the initial value problem. We also determine the Burton stability of such equations. The arbitrary order case is taken in the sense of Riemann-Liouville fractional operators.

Highlights

1 Introduction Fractional calculus is an area of specialization in mathematics that is concerned with differential and integral operators of arbitrary orders
Fractional derivatives are mainly used with classical integer order patterns, in which such effects are neglected
The significance of fractional derivatives is manifested in modeling, electrical properties of real materials, capacity of rheological properties of rocks, and many other fields

Summary

Introduction

Fractional calculus is an area of specialization in mathematics that is concerned with differential and integral operators of arbitrary orders. Existence and uniqueness theory is studied widely in fractional differential equations. Agarwal et al studied the existence of solutions for the Riemann-Liouville operator for a class of integro-differential equations of high fractional order [ ].

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