On generalized fractional operators and related function spaces with applications

Abstract

The application of fractional calculus-based mathematical models in physics is a well-established practice. However, a challenge arises due to the variety of fractional operators used in these models and the search for solutions in different function spaces. This paper proposes a unified approach to this issue by applying general fractional operators that can capture and extend previous attempts, with appropriate parameters that align with the features of the phenomena being modeled. The main goal is to establish invariant spaces for these operators. This will simplify the application of various proof techniques.