Existence of solutions for nonlinear problems involving mixed fractional derivatives with \(p(x)\)-Laplacian operator
type: Item
instance of: scholarly article
title: Existence of solutions for nonlinear problems involving mixed fractional derivatives with \(p(x)\)-Laplacian operator
author: Bingzhi Sun
published in: Demonstratio Mathematica
publication date: 2024-08-21T00:00:00Z
review text: Resonance problems are among the most intriguing and widely studied topics in the field of differential boundary value problems (BVPs). In the present paper, the authors get the existence of solutions for the functional BVP (1.1) involving the mixed fractional derivatives with the \(p(x)\)-Laplacian operator in the case of non-resonance and the case of resonance. Here, the \(p(x)\)-Laplacian operator is a generalization of the \(p\)-Laplacian operator. The authors establish the solvability results of the problem for the non-resonant case using the Banach fixed point theorem and demonstrate the existence of solutions in the resonance case through an extended version of Mawhin's coincidence theory. The existence of solutions for the functional BVPs for mixed fractional differential equation with the \(p(x)\)-Laplacian has not been studied and contributes to the theoretical and applied nature. Also, several examples are provided to validate the main results.
reviewed by: Tuğba Şenlik Çerdik
Mathematics Subject Classification ID: 34A08
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 47H11
zbMATH DE Number: 7899060
zbMATH Keywords: functional boundary condition
zbMATH Keywords: \(p(x)\)-Laplacian
zbMATH Keywords: mixed fractional derivatives
zbMATH Keywords: fixed point theorem
zbMATH Keywords: coincidence degree theory
MaRDI profile type: Publication
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DOI: 10.1515/DEMA-2024-0045
description: scientific article; zbMATH DE number 7899060