Topic of Research Seminar: Transmuted fractional calculus with general analytic kernels

Abstract: In fractional calculus, many different theories have been proposed with different kernels, be it singular or non-singular. One such theory is with analytic kernels. In this paper, we aim to combine this concept with another important notion in fractional calculus: the transmuted fractional calculus. This results in the construction of a general class of fractional calculus named as the transmuted fractional calculus with general analytic kernels. The fundamental properties and behaviour of the newly-established transmuted operators have been discussed for left-sided and right-sided fractional calculus. This paper also extends this theory to fractional calculus with respect to functions, weighted fractional calculus, and the combination of these prior-mentioned classes. Using the transmuted operators with analytic kernels we have also introduced a generalised Laplace transform.

Joint work with Khadija Bibi (National University of Science and Technology, Islamabad, Pakistan).

Subject Field of Topic: Fractional Calculus

Name of Speaker: Haniyyah Ul Irshad

Professorial Rank of Speaker: MS Student

Email of Speaker: [email protected]

Affiliation of Speaker: School of Natural Sciences, SNS – NUST

Date and Venue: (Wednesday) 11 Sep 2024, 15:30 hrs, at CR #202 (New SNS Building), School of Natural Sciences, NUST Islamabad