Solvability of Mixed Problems for a Fourth-Order Equation with Involution and Fractional Derivative-Reference-Cited by-同舟云学术

Solvability of Mixed Problems for a Fourth-Order Equation with Involution and Fractional Derivative

Published:2023-01-30 Issue:2 Volume:7 Page:131
ISSN:2504-3110
Container-title:Fractal and Fractional
language:en
Short-container-title:Fractal Fract

Author:

Kirane Mokhtar¹^ORCID,Sarsenbi Abdissalam A.²^ORCID

Affiliation:

1. Département de Mathématiques, Université de La Rochelle, 17042 La Rochelle, France

2. Department of Mathematics, M. Auezov South Kazakhstan University, Shymkent 160000, Kazakhstan

Abstract

In the present work, two-dimensional mixed problems with the Caputo fractional order differential operator are studied using the Fourier method of separation of variables. The equation contains a linear transformation of involution in the second derivative. The considered problem generalizes some previous problems formulated for some fourth-order parabolic-type equations. The basic properties of the eigenfunctions of the corresponding spectral problems, when they are defined as the products of two systems of eigenfunctions, are studied. The existence and uniqueness of the solution to the formulated problem is proved.

Funder

Ministry of Science and Education of the Republic of Kazakhstan

Publisher

MDPI AG

Subject

Statistics and Probability,Statistical and Nonlinear Physics,Analysis

Link

https://www.mdpi.com/2504-3110/7/2/131/pdf

Reference33 articles.

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2. Przeworska-Rolewicz, D. (1973). Equations with Transformed Argument. An Algebraic Approach, Elsevier-PWN. [1st ed.].

3. Cabada, A., and Tojo, F.A.F. (2015). Differential Equations with Involutions, Atlantis Press. [1st ed.].