On some analytic properties of tempered fractional calculus

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.

16 pages

References in corpus (1)

• On some new properties of fractional derivatives with Mittag-Leffler kernel

Cited by in corpus (4)

• On tempered fractional calculus with respect to functions and the associated fractional differential equations
• Finite time stability of tempered fractional systems with time delays
• Optimal Control Problems Involving Combined Fractional Operators with General Analytic Kernels
• Weak Pontryagin's Maximum Principle for Optimal Control Problems Involving a General Analytic Kernel