Fractional neutral evolution equations with nonlocal conditions

Hamdy M Ahmed

doi:10.1186/1687-1847-2013-117

Abstract

In the present paper, we deal with the fractional neutral differential equations involving nonlocal initial conditions. The existence of mild solutions are established. The results are obtained by using the fractional power of operators and the Sadovskii’s fixed point theorem. An application to a fractional partial differential equation with nonlocal initial condition is also considered. MSC:26A33, 34K30, 34K37, 34K40.

Highlights

1 Introduction The nonlocal condition, which is a generalization of the classical condition, was motivated by physical problems
Existence results for semilinear evolution equations with nonlocal conditions were investigated in [ – ]
Fractional differential equations describe many practical dynamical phenomena arising in engineering, physics, economy and science

Summary

Introduction

The nonlocal condition, which is a generalization of the classical condition, was motivated by physical problems. The main purpose of this paper is to study the existence of mild solutions of semilinear neutral fractional differential equations with nonlocal conditions in the following form cDα x(t) + F t, x(t), x b (t) , .

Objectives

Results

Conclusion