The fractional evolution equations associated with the quantum fractional number operator

Abstract

The Liouville–Caputo and Riemann–Liouville fractional derivatives have been two of the most useful operators for modeling nonlocal behaviors by fractional differential equations. In terms of Mittag–Leffler function and convolution product, using the Laplace transform, we give the exact values of the solutions of the Liouville–Caputo and Riemann–Liouville time fractional evolution equations associated with the Quantum fractional number operator. Therefore, we study the attractiveness of these solutions.