Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

New Study of Existence and Dimension of the Set of Solutions for Nonlocal Impulsive Differential Inclusions With Sectorial Operator

Version 1 : Received: 20 February 2021 / Approved: 23 February 2021 / Online: 23 February 2021 (14:16:13 CET)

A peer-reviewed article of this Preprint also exists.

Alsarori, N.; Ghadle, K.; Sessa, S.; Saleh, H.; Alabiad, S. New Study of the Existence and Dimension of the Set of Solutions for Nonlocal Impulsive Differential Inclusions with a Sectorial Operator. Symmetry 2021, 13, 491. Alsarori, N.; Ghadle, K.; Sessa, S.; Saleh, H.; Alabiad, S. New Study of the Existence and Dimension of the Set of Solutions for Nonlocal Impulsive Differential Inclusions with a Sectorial Operator. Symmetry 2021, 13, 491.

Journal reference: Symmetry 2021, 13, 491
DOI: 10.3390/sym13030491

Abstract

In this article, we are interested in a new generic class of nonlocal fractional impulsive differential inclusions with linear sectorial operator and Lipschitz multivalued function in the setting of finite dimensional Banach spaces. By modifying the definition of PC-mild solutions initiated by Shu, we succeeded to determine new conditions that sufficiently guarantee the existence of the solutions. The results are obtained by combining techniques of fractional calculus and fixed point theorem for contraction maps. We also characterize the topological structure of the set of solutions. Finally, we provide a demonstration to address the applicability of the theoretical results.

Subject Areas

Impulsive fractional differential inclusions; Nonlocal conditions; Fixed point theorems; 10 Mild solutions

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