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arXiv · 1912.05482

On some analytic properties of tempered fractional calculus

Arran Fernandez·Ceren Ustaoglu
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Abstract

We consider the integral and derivative operators of tempered fractional calculus, and examine their analytic properties. We discover connections with the classical Riemann-Liouville fractional calculus and demonstrate how the operators may be used to obtain special functions such as hypergeometric and Appell's functions. We also prove an analogue of Taylor's theorem and some integral inequalities to enrich the mathematical theory of tempered fractional calculus.

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Arran Fernandez, Ceren Ustaoglu. 2019-12-11. On some analytic properties of tempered fractional calculus. https://doi.org/10.1016/j.cam.2019.112400

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