ON FRACTIONAL INTEGRALS AND DERIVATIVES OF A FUNCTION WITH RESPECT TO ANOTHER FUNCTION-Reference-Cited by-同舟云学术

ON FRACTIONAL INTEGRALS AND DERIVATIVES OF A FUNCTION WITH RESPECT TO ANOTHER FUNCTION

Published:2023-01 Issue:04 Volume:31 Page:
ISSN:0218-348X
Container-title:Fractals
language:en
Short-container-title:Fractals

Author:

NIETO JUAN J.¹,ALGHANMI MADEAHA²³,AHMAD BASHIR³,ALSAEDI AHMED³,ALHARBI BOSHRA³

Affiliation:

1. CITMAga, Departamento de Estatística, Análise Matemática e Optimización, University of Santiago de Compostela, Santiago de Compostela 15782, Spain

2. Department of Mathematics, College of Sciences and Arts, King Abdulaziz University, Rabigh 21911, Saudi Arabia

3. Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia

Abstract

In this paper, we present new definitions of generalized fractional integrals and derivatives with respect to another function and derive some of their properties, such as their inter-relationship and semigroup law. Caputo-type generalized fractional derivative with respect to another function is also defined and its properties are derived. A Cauchy problem involving the new Caputo-type generalized fractional derivative is also studied. We also provide an expansion formula for Caputo-type derivative and apply it to solve a fractional-order problem.

Funder

Agencia Estatal de Investigacion

Xunta de Galicia

Publisher

World Scientific Pub Co Pte Ltd

Subject

Applied Mathematics,Geometry and Topology,Modeling and Simulation

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218348X23400662

Reference32 articles.

1. Numerical analysis of the fractional evolution model for heat flow in materials with memory

2. A numerical study of fractional rheological models and fractional Newell-Whitehead-Segel equation with non-local and non-singular kernel

3. Numerical solutions of time-fractional Klein-Gordon equations by clique polynomials

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