New generalized integral transform via Dzherbashian-Nersesian fractional operator

Rachid Belgacem; Ahmed Bokhari; Dumitru  Baleanu; Salih  Djilali

doi:10.11121/ijocta.1449

Authors

Rachid Belgacem Department of Mathematics, Hassiba Benbouali University, Chlef, Algeria
Ahmed Bokhari Department of Mathematics, Hassiba Benbouali University, Chlef, Algeria
Dumitru Baleanu Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon
Salih Djilali Department of Mathematics, Hassiba Benbouali University, Chlef, Algeria

DOI:

https://doi.org/10.11121/ijocta.1449

Keywords:

Fractional Dzherbashian--Nersesian operator, Fractional derivatives, Integral transform, Jafari transform, Cauchy-type problems

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.

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Author Biographies

Rachid Belgacem, Department of Mathematics, Hassiba Benbouali University, Chlef, Algeria

Rachid Belgacem's academic career began with a Diploma of Higher Studies in Mathematics, specializing in Operational Research, from the Houari Boumediene University of Sciences and Technologies (USTHB) in Algiers, Algeria, in 1999. He then obtained his Magister degree in Mathematics in 2012, from the University of Mostaganem. Subsequently, he obtained his doctorate in mathematics, specializing in optimization and optimal control, at the same university. Belgacem obtained his Habilitation (HDR) on July 6, 2021, where his research interests were focused on fractional calculus, optimal control, numerical optimization and applied mathematics. Currently, Belgacem is an associate professor in the Department of Mathematics of the Faculty of Exact Sciences and Computer Science of Hassiba Benbouali University of Chlef, Algeria.

Ahmed Bokhari, Department of Mathematics, Hassiba Benbouali University, Chlef, Algeria

Ahmed Bokhari is an Associate Professor at the Department of Mathematics, Exact Sciences, and Informatics Faculty, Hassiba Benbouali University of Chelef, Algeria. He received his magister (2012) and Ph.D. (2017) degrees from the Department of Mathematics, Mostaganem University, Algeria. His research areas include optimization, optimal control, and fractional differential equations.

Dumitru Baleanu, Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon

Dumitru Baleanu is a Professor of mathematics in the Computer Science and Mathematics Department, Lebanese American University, Beirut. He received his B.Sc. from the University of Craiova, M.Sc. from the University of Bucharest, and obtained his Ph.D. from the Institute of Atomic Physics, Romania. Dr. Baleanu is a pioneer of the fractional variational principles and their applications in control theory. His research areas include fractional differential equations.

Salih Djilali, Department of Mathematics, Hassiba Benbouali University, Chlef, Algeria

Salih Djilali is an Associate Professor in the Department of Mathematics at the University of Chlef. He obtained his Ph.D. from the University of Tlemcen in 2018. Dr. Djilali's current research focuses on applied mathematics, employing various methodologies such as partial differential equations, delay differential equations, and fractional calculus.

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