Differintegration with Respect to Functions in Fractional Models Involving Mittag-Leffler Functions

5 Pages Posted: 13 Nov 2018

See all articles by Arran Fernandez

Arran Fernandez

University of Cambridge

Dumitru Baleanu

Çankaya University

Date Written: July 1, 2018

Abstract

We consider what it means to fractionally differentiate or integrate one function with respect to another function, in models of fractional calculus which involve Mittag-Leffler kernels. Using our presented definitions, we derive series expressions for such differ-integrals, which we then use to prove some important results such as an elegant formulation of the fractional chain rule.

Suggested Citation

Fernandez, Arran and Baleanu, Dumitru, Differintegration with Respect to Functions in Fractional Models Involving Mittag-Leffler Functions (July 1, 2018). Proceedings of International Conference on Fractional Differentiation and its Applications (ICFDA) 2018, Available at SSRN: https://ssrn.com/abstract=3275746 or http://dx.doi.org/10.2139/ssrn.3275746

Arran Fernandez (Contact Author)

University of Cambridge ( email )

Trinity Ln
Cambridge, CB2 1TN
United Kingdom

Dumitru Baleanu

Çankaya University ( email )

Turkey

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