AccScience Publishing / IJOCTA / Volume 14 / Issue 2 / DOI: 10.11121/ijocta.1449
RESEARCH ARTICLE

New generalized integral transform via Dzherbashian-Nersesian fractional operator

Rachid Belgacem1 Ahmed Bokhari1* Dumitru Baleanu2,3 Salih Djilali1
IJOCTA 2024, 14(2), 90–98; https://doi.org/10.11121/ijocta.1449
Submitted: 20 August 2023 | Accepted: 7 November 2023 | Published: 18 March 2024
© 2024 by the Author(s). This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution -Noncommercial 4.0 International License (CC-by the license) ( https://creativecommons.org/licenses/by-nc/4.0/ )
Abstract

In this paper, we derive a new generalized integral transform on Dzherbashian–Nersesian fractional operator and give some special cases. We make a generalization of the application of integral transformations to different fractional operators, where several previous results can be invoked from a single relation. We also use the new results obtained to solve some fractional differential equations involving the recent revival of Dzherbashian-Nersesian fractional operators.

Keywords
Fractional Dzherbashian--Nersesian operator
Fractional derivatives
Integral transform
Jafari transform
Cauchy-type problems
Conflict of interest
The authors declare they have no competing interests.
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