Integro-Differential Boundary Conditions to the Sequential ψ1-Hilfer and ψ2-Caputo Fractional Differential Equations-Reference-Cited by-同舟云学术

Integro-Differential Boundary Conditions to the Sequential ψ1-Hilfer and ψ2-Caputo Fractional Differential Equations

Published:2023-02-08 Issue:4 Volume:11 Page:867
ISSN:2227-7390
Container-title:Mathematics
language:en
Short-container-title:Mathematics

Author:

Sitho Surang¹,Ntouyas Sotiris K.²^ORCID,Sudprasert Chayapat³,Tariboon Jessada³^ORCID

Affiliation:

1. Department of Social and Applied Science, College of Industrial Technology, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand

2. Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece

3. Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand

Abstract

In this paper, we introduce and study a new class of boundary value problems, consisting of a mixed-type ψ1-Hilfer and ψ2-Caputo fractional order differential equation supplemented with integro-differential nonlocal boundary conditions. The uniqueness of solutions is achieved via the Banach contraction principle, while the existence of results is established by using the Leray–Schauder nonlinear alternative. Numerical examples are constructed illustrating the obtained results.

Funder

King Mongkut's University of Technology North Bangkok

Publisher

MDPI AG

Subject

General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)

Link

https://www.mdpi.com/2227-7390/11/4/867/pdf

Reference23 articles.

1. Damping description involving fractional operators;Gaul;Mech. Syst. Signal Process.,1991

2. A fractional calculus approach of self-similar protein dynamics;Glockle;Biophys. J.,1995

3. Experimental evidence for fractional time evolution in glass forming materials;Hilfer;J. Chem. Phys.,2002

4. Carpinteri, A., and Mainardi, F. (1997). Fractals and Fractional Calculus in Continuum Mechanics, Springer.

5. Relaxation in filled polymers: A fractional calculus approach;Metzler;J. Chem. Phys.,1995

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