Work

Equivalence Between Fractional Differential Problems and Their Corresponding Integral Forms with the Pettis Integral

Year: 2024

Type: article

Abstract: The problem of equivalence between differential and integral problems is absolutely crucial when applying solution methods based on operators and their properties in function spaces. In this paper, we complement the solution of this important problem by considering the case of general derivatives and integrals of fractional order for vector functions for weak topology. Even if a Caputo differential fractional order problem has a right-hand side that is weakly continuous, the equivalence between the differential and integral forms may be affected. In this paper, we present a complete solution to this problem using fractional order Pettis integrals and suitably defined pseudo-derivatives, taking care to construct appropriate Hölder-type spaces on which the operators under study are mutually inverse. In this paper, we prove, in a number of cases, the equivalence of differential and integral problems in Hölder spaces and, by means of appropriate counter-examples, investigate cases where this property of the problems is absent.

Source: Mathematics

DOI: 10.3390/math12233642

Authors: Mieczysław Cichoń, Wafa Shammakh, Kinga Cichoń, Hussein A. H. Salem

Institutions: Adam Mickiewicz University in Poznań, University of Jeddah, Poznań University of Technology, Alexandria University

Language: English

Topic: Nonlinear Differential Equations Analysis

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,955

OpenAlex ID: W4404592385

FWCI: 0.765

Cites: 37

Cited by: 1

Related to: 10