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

Juan J. Nieto, Madeaha Alghanmi, Bashir Ahmad, Ahmed Alsaedi and Boshra Alharbi
Additional contact information
Juan J. Nieto: CITMAga, Departamento de Estatística, Análise Matemática e Optimización, University of Santiago de Compostela, Santiago de Compostela 15782, Spain
Madeaha Alghanmi: ��Department of Mathematics, College of Sciences and Arts, King Abdulaziz University, Rabigh 21911, Saudi Arabia‡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
Bashir Ahmad: ��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
Ahmed Alsaedi: ��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
Boshra Alharbi: ��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

FRACTALS (fractals), 2023, vol. 31, issue 04, 1-15

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.

Keywords: Fractional Calculus; Generalized Fractional Integral; Caputo-Type Fractional Derivative; Fractional Differential Equations; Existence (search for similar items in EconPapers)
Date: 2023
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.worldscientific.com/doi/abs/10.1142/S0218348X23400662
Access to full text is restricted to subscribers

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wsi:fracta:v:31:y:2023:i:04:n:s0218348x23400662

Ordering information: This journal article can be ordered from

DOI: 10.1142/S0218348X23400662

Access Statistics for this article

FRACTALS (fractals) is currently edited by Tara Taylor

More articles in FRACTALS (fractals) from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().