SOME SYMMETRIC PROPERTIES AND APPLICATIONS OF WEIGHTED FRACTIONAL INTEGRAL OPERATOR

Shanhe Wu (), Muhammad Samraiz, Ahsan Mehmood (), Fahd Jarad and Saima Naheed ()
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Shanhe Wu: Department of Mathematics, Longyan University, Longyan 364012, P. R. China
Muhammad Samraiz: Department of Mathematics, University of Sargodha, 40100 Sargodha, Pakistan
Ahsan Mehmood: Department of Mathematics, University of Sargodha, 40100 Sargodha, Pakistan
Fahd Jarad: Department of Mathematics, Cankaya University, 06790 Etimesgut, Ankara, Turkey4Department of Medical Research, China Medical University, Taichung 40402, Taiwan
Saima Naheed: Department of Mathematics, University of Sargodha, 40100 Sargodha, Pakistan

FRACTALS (fractals), 2023, vol. 31, issue 10, 1-12

Abstract: In this paper, a weighted generalized fractional integral operator based on the Mittag-Leffler function is established, and it exhibits symmetric characteristics concerning classical operators. We demonstrate the semigroup property as well as the boundedness of the operator in absolute continuous like spaces. In this work, some applications with graphical representation are also considered. Finally, we modify the weighted generalized Laplace transform and then applied it to the newly defined weighted fractional integral operator. The defined operator is an extension and generalization of classical Riemann–Liouville and Prabhakar integral operators.

Keywords: Mittag-Leffler Function; Symmetric Properties; Weighted Fractional Integral; Weighted Laplace Transform; Modified (k; s)-fractional Integral (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0218348X2340011X

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