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ON THE WEIGHTED FRACTIONAL OPERATORS OF A FUNCTION WITH RESPECT TO ANOTHER FUNCTION

F. JARAD

Çankaya University, Department of Mathematics, 06790 Etimesgut, Ankara, Turkey

E-mail Address: fahd@cankaya.edu.tr

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T. ABDELJAWAD

Department of Mathematics and General Sciences, Prince Sultan University, P. O. Box 66833, Riyadh 11586, Saudi Arabia

Department of Medical Research, China Medical University, Taichung 40402, Taiwan

Department of Computer Science and Information Engineering, Asia University, Taichung, Taiwan

E-mail Address: tabdeljawad@psu.edu.sa

Corresponding author.

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, and

K. SHAH

Department of Mathematics, University of Malakand, Khyber Pakhtunkhwa, Pakistan

E-mail Address: kamalshah408@gmail.com

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https://doi.org/10.1142/S0218348X20400113Cited by:72 (Source: Crossref)

This article is part of the issue:

Special Issue on Fractal and Fractional with Applications to Nature
Guest Editors: Abdon Atangana, Emile Franc Goufo Ndongmo, José Francisco Gómez Aguilar, Muhammad Altaf Khan and Ilknur Koca

Abstract

The primary goal of this study is to define the weighted fractional operators on some spaces. We first prove that the weighted integrals are bounded in certain spaces. Afterwards, we discuss the weighted fractional derivatives defined on absolute continuous-like spaces. At the end, we present a modified Laplace transform that can be applied perfectly to such operators.

Keywords:

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Vol. 28, No. 08

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History

Received 27 December 2019

Accepted 1 March 2020

Published: June 25, 2020

Information

This is an Open Access article in the “Special Issue on Fractal and Fractional with Applications to Nature” published by World Scientific Publishing Company. It is distributed under the terms of the Creative Commons Attribution 4.0 (CC BY) License which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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ON THE WEIGHTED FRACTIONAL OPERATORS OF A FUNCTION WITH RESPECT TO ANOTHER FUNCTION

Abstract

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