A nonlocal multi-point multi-term fractional boundary value problem with Riemann-Liouville type integral boundary conditions involving two indices

Ahmed Alsaedi,Sotiris K Ntouyas,Ravi P Agarwal,Bashir Ahmad

doi:10.1186/1687-1847-2013-369

Abstract

Abstract In this paper, we study the existence of solutions for fractional differential equations of arbitrary order with multi-point multi-term Riemann-Liouville type integral boundary conditions involving two indices. The Riemann-Liouville type integral boundary conditions considered in the problem address a more general situation in contrast to the case of a single index. Our results are based on standard fixed point theorems. Some illustrative examples are also presented. MSC:26A33, 34A08.

Highlights

1 Introduction In the last few decades, the subject of fractional differential equations has become a hot topic for the researchers due to its intensive development and applications in the field of physics, mechanics, chemistry, engineering, etc
A fractional-order differential operator distinguishes itself from the integer-order differential operator in the sense that it is nonlocal in nature, that is, the future state of a dynamical system or process involving fractional derivative depends on its current state as well its past states
We study a boundary value problem of fractional differential equations of arbitrary order q ∈

Summary

Introduction

In the last few decades, the subject of fractional differential equations has become a hot topic for the researchers due to its intensive development and applications in the field of physics, mechanics, chemistry, engineering, etc. Sudsutad and Tariboon [ ] obtained some existence results for an integro-differential equation of fractional order q ∈ We study a boundary value problem of fractional differential equations of arbitrary order q ∈ Where cDq denotes the Caputo fractional derivative of order q, f is a given continuous function, [Ikj,i x]|ηηii– = [Ikj,i x](ηi) – [Ikj,i x](ηi– ), Ikj,i is the Riemann-Liouville fractional integral of order kj,i > , j = , , .

Results

Conclusion