On multi-order fractional differential operators in the unit disk

Abstract

In this article, we generalize fractional operators (differential and integral ) in the unit
disk. These operators are generalized the Srivastava-Owa operators. Geometric properties are studied
and the advantages of these operators are discussed. As an application, we impose a method, involving
a memory formalism of the Beer-Lambert equation based on a new generalized fractional differential
operator. We give solutions in terms of the multi-index Mittag-Leer function. In addition, we sanctify
the out come from a stochastic standpoint. We utilize the generalized Wright function to obtain the
analytic formula of solutions.
Keywords: analytic function; fractional calculus; fractional differential equation; unit disk