Multiplicative fractional integrals and derivatives for two-variable functions

This research examines the relationships between fractional calculus, a field that has recently attracted considerable research interest, and multiplicative calculus. In the Introduction, the arithmetic structure of multiplicative calculus is examined, along with the fundamental operational operators and their systematics. Additionally, the construction of generator functions and their role in deriving new arithmetic frameworks are demonstrated, with examples of alternative arithmetic systems provided. The Preliminaries present the fundamental concepts, definitions, and theorems of multiplicative calculus, including its derivative and integral operators. Subsequently, we present the main results obtained in this study. We introduce, for the first time, multiplicative fractional integral and derivative operators for functions of two variables. Subsequently, we establish several important properties of the proposed multiplicative fractional operators. Finally, we present some examples and graphical illustrations to demonstrate applications of these operators.