On bivariate fractional calculus with general univariate analytic kernels

Sunday Simon Isah, Arran Fernandez and Mehmet Ali Özarslan

Chaos, Solitons & Fractals, 2023, vol. 171, issue C

Abstract: We introduce a general bivariate fractional calculus, defined using a kernel based on an arbitrary univariate analytic function with an appropriate bivariate substitution. Various properties of the introduced general operators are established, including a series formula, function space mappings, and Fourier and Laplace transforms. A major result of this paper is a fractional Leibniz rule for the new operators, the derivation of which involves correcting a minor error in one of the classic textbooks on fractional calculus. We also solve some fractional differential equations using transform methods, revealing an interesting connection between bivariate type Mittag-Leffler functions.

Keywords: Bivariate fractional calculus; Fractional integral operators; Analytic kernel functions; Leibniz rule; Double Laplace transforms (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:171:y:2023:i:c:s096007792300396x

DOI: 10.1016/j.chaos.2023.113495

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