Nonlinear Sequential Riemann-Liouville and Caputo Fractional Differential Equations with Nonlocal and Integral Boundary Conditions

Suphawat Asawasamrit ,Nawapol Phuangthong ,Sotiris K Ntouyas ,Jessada Tariboon

doi:10.28924/2291-8639-17-2019-47

Abstract

In this paper, we discuss the existence and uniqueness of solutions for a new class of sequential fractional differential equations of Riemann-Liouville and Caputo types with nonlocal integral boundary conditions, by using standard fixed point theorems. We also demonstrate the application of the obtained results with the aid of examples.

Highlights

Fractional differential equations have gained considerable importance due to their widespread applications in various disciplines of social and natural sciences, and engineering
There has been a significant development in fractional calculus and fractional differential equations, for instance, see the monographs by Kilbas et al [12], Lakshmikantham et al [14], Miller and Ross [15], Podlubny [16], Samko et al [18], Diethelm [9], Ahmad et al [7] and the papers [1, 4,5,6, 8, 10, 17, 20, 21]
In [2] the authors studied a class of nonlinear differential equations with multiple fractional derivatives and Caputo type integro-differential boundary conditions

Summary

Introduction

Fractional differential equations have gained considerable importance due to their widespread applications in various disciplines of social and natural sciences, and engineering. Fractional derivatives; fractional integral; boundary value problems; existence; uniqueness; fixed point theorems. The uniqueness result for the problem (1.1) is obtained by means of a celebrated fixed point theorem due to Banach.

Results

Conclusion