Topic of Research Seminar: Bivariate Fractional Calculus with General Bivariate Analytic Kernels

Abstract: We use a general bivariate analytic function with fractional power substitutions to define a bivariate fractional integral operator which can be expressed as a double infinite sum of classical Riemann-Liouville operators, using analyticity, which allows many interesting and useful fundamental properties. We further consider inversion properties of our proposed model, which in turn motivate the definition of a bivariate fractional derivative operator based on the same bivariate analytic kernels modified by fractional powers. We then prove the analogues of the fundamental theorems of calculus, Leibniz rule, and consider the functional maps and bounds, Laplace, and Fourier transforms in this model of bivariate fractional calculus. As an application, we consider some illustrative examples which have already found applications in the literature using our new model.

Subject Field of Topic: Fractional Calculus

Name of Speaker: Sunday Simon Isah

Professorial Rank of Speaker: PhD Scholar

Email of Speaker: [email protected]

Affiliation of Speaker: Eastern Mediterranean University, Cyprus

Date and Venue: (Wednesday) 25 Sep 2024, 15:30 hrs, at CR #202 (New SNS Building). School of Natural Sciences, NUST Islamabad