On fractional calculus with general analytic kernels

Arran Fernandez, Mehmet Ali Özarslan and Dumitru Baleanu

Applied Mathematics and Computation, 2019, vol. 354, issue C, 248-265

Abstract: Many possible definitions have been proposed for fractional derivatives and integrals, starting from the classical Riemann–Liouville formula and its generalisations and modifying it by replacing the power function kernel with other kernel functions. We demonstrate, under some assumptions, how all of these modifications can be considered as special cases of a single, unifying, model of fractional calculus. We provide a fundamental connection with classical fractional calculus by writing these general fractional operators in terms of the original Riemann–Liouville fractional integral operator. We also consider inversion properties of the new operators, prove analogues of the Leibniz and chain rules in this model of fractional calculus, and solve some fractional differential equations using the new operators.

Keywords: Fractional calculus; Special functions; Convergent series; Ordinary differential equation; Volterra integral equation (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (20)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:354:y:2019:i:c:p:248-265

DOI: 10.1016/j.amc.2019.02.045

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