Analytic solutions of a generalized complex multi-dimensional system with fractional order

Abstract

The Duhamel principle is a mathematical principle that allows us to solve linear partial differential equations. This system is generalized by the concept of the kk-symbol fractional calculus. We demonstrate that in specific functional domains, the suggested system produces a global solution. Convergence toward the stable point is investigated. Some special cases are illustrated including the rotated Koebe function, which is used for creating the optimal solutions, where these functions are convex univalent in the open unit disk.

Keywords

• fractional differential equations
• fractional differential operator
• k-symbol calculus
• fractional calculus
• analytic functions
• the cauchy-schwartz inequality
• 30c45
• 30c55