Abstract
In this paper, we aim to generalize a fractional integro-differential operator in the open unit disk utilizing Jackson calculus (quantum calculus or q-calculus). Next, by consuming the generalized operator to define a formula of normalized analytic functions, we present a set of integral inequalities using the concepts of subordination and superordination. In addition, as an application, we determine the maximum and minimum solutions of the extended fractional 2D-shallow water equation in a complex domain.
Highlights
Equation in a Complex Domain.Elementary series and polynomials, the Mittag–Leffler functions and polynomials and their consequences, can be frequently seen in specific areas of number theory, including the theory of partitions
We employ the definition of the q- Mittag–Leffler functions to modify a fractional integral operator of a complex variable
We investigate a generalization of fractional integro-differential operators in the open unit disk formulated by the q-calculus
Summary
We employ the definition of the q- Mittag–Leffler functions to modify a fractional integral operator of a complex variable. The. SWEs can be used to study numerous physical phenomena of interest, such as storm surges, tidal variations, tsunami waves, and forces performing on off-shore assemblies, and can be joined to transport equations to formulate transport of chemical species. SWEs can be used to study numerous physical phenomena of interest, such as storm surges, tidal variations, tsunami waves, and forces performing on off-shore assemblies, and can be joined to transport equations to formulate transport of chemical species Most of these equations are solved by numerical techniques [8,9]. As an application, we compute the maximum and minimum solutions of the modified fractional 2D-shallow water equation in a complex domain
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
