The Extension of Euler’s Theorem on Homogeneous Functions Using Katugampola Fractional Differential Operators

Abstract

The Katugampola fractional derivative for functions of two variables, is a mathematical tool with significant applications in solving diffusion problems, fluid dynamics, wave propagation, signal processing, etc. This paper deals with the new results of a Katugampola fractional partial derivatives and its properties. Starting with basic results of Katugampola derivatives, we study corresponding partial derivatives and its properties. We obtained a generalized form of Euler’s theorem on homogeneous function. Finally, we illustrate our results with examples.