Semilinear fractional evolution inclusion problem in the frame of a generalized Caputo operator
type: Item
instance of: scholarly article
title: Semilinear fractional evolution inclusion problem in the frame of a generalized Caputo operator
zbMATH Open document ID: 1484.34028
DOI: 10.1155/2021/8162890
author: Adel Lachouri
author: Abdelouaheb Ardjouni
author: F. Jarad
author: Mohammed S. Abdo
published in: Journal of Function Spaces
publication date: 2021-12-16T00:00:00Z
review text: Summary: In this paper, we study the existence of solutions to initial value problems for a nonlinear generalized Caputo fractional differential inclusion with Lipschitz set-valued functions. The applied fractional operator is given by the kernel \(k(\rho, s)=\xi(\rho)-\xi(s)\) and the derivative operator \((1/\xi^\prime(\rho))(d/d\rho)\). The existence result is obtained via fixed point theorems due to Covitz and Nadler. Moreover, we also characterize the topological properties of the set of solutions for such inclusions. The obtained results generalize previous works in the literature, where the classical Caputo fractional derivative is considered. In the end, an example demonstrating the effectiveness of the theoretical results is presented.
Mathematics Subject Classification ID: 34A08
Mathematics Subject Classification ID: 34A12
Mathematics Subject Classification ID: 34A60
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 7446743
zbMATH Keywords: fixed point theorem
zbMATH Keywords: generalized Caputo fractional differential inclusion
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2021/8162890
OpenAlex ID: W3207981576
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description: scientific article; zbMATH DE number 7446743