On some analytic properties of tempered fractional calculus
arXiv:1912.05482 · doi:10.1016/j.cam.2019.112400
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.
arXiv comment16 pages
References in corpus (4)
- On some new properties of fractional derivatives with Mittag-Leffler kernel
- A new fractional derivative without singular kernel: Application to the modelling of the steady heat flow
- On fractional calculus with general analytic kernels
- Series representations for fractional-calculus operators involving generalised Mittag-Leffler functions
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