Abstract
The aim of this paper is to give existence results for a class of coupled systems of fractional integrodifferential equations with Hilfer fractional derivative in Banach spaces. We first give some definitions, namely the Hilfer fractional derivative and the Hausdorff’s measure of noncompactness and the Sadovskii’s fixed point theorem.
Highlights
Fractional differential equations have been a good tool in many research areas in the last decade, such as engineering, mathematics, physics, and many other sciences [1, 2]
A lot of attention has been devoted to the existence of fractional differential problems with Hilfer fractional derivative, see [10,11,12]
The Hilfer fractional derivative, which is a generalization of the RiemannLiouville fractional derivative, was introduced by nonother than Hilfer [1, 13]
Summary
Fractional differential equations have been a good tool in many research areas in the last decade, such as engineering, mathematics, physics, and many other sciences [1, 2]. The first results on the existence of general value problems involving Hilfer fractional derivative were investigated in [14] and after that in [12] Following these results, Gu and Trujilo [15] gave the existence of solutions for fractional differential equations with Hilfer fractional derivative using the notion of measure of noncompactness. Fractional differential equations (FDEs) involving Caputo’s fractional derivative are commonly considered with impulsive conditions for obtaining mild solutions [17,18,19,20]. To make a little contribution to the already existing results, we consider in this paper a class of coupled systems of Hilfer fractional differential equations with not instantaneous impulses in a Banach space as follows: Advances in Mathematical Physics. This paper is organized as follows: we first give some preliminaries and notions that will be used throughout the work; after that, we will establish the existence results by means of the fixed point theory; last but not least, we will give an example that illustrates the results
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