Hybrid Fractional Operators: A New Approach with Proportional Derivatives

Abstract

In this paper, new hybrid fractional operators are introduced, which are generated by replacing classical derivatives with proportional derivatives. To be more precise, we combine regularised Hilfer-Prabhakar (RHP) and two-parameter Atangana-Baleanu (SABC) fractional derivatives with constant proportional derivatives. This paper provides an in-depth analysis of the implications and uses of these hybrid operators as they relate to differential equations with constant proportional derivatives.