Generalized Composite Fractional Derivatives and Integral Operators With Incomplete R‐Function Kernels

Fractional differential equations (FDEs) have received a lot of interest because of their diverse applications in engineering, mathematical physics, chemistry, and biology. This study introduces a new family of fractional integral operators using incomplete R‐function kernels, advancing the theoretical foundation of FDEs further. These operators are built on the foundation of generalized composite fractional derivatives, providing an enlarged structure that can support a greater range of solutions. The proposed framework not only generalizes existing models but also adds new analytical tools to fractional calculus. Several specific situations and corollaries are provided to demonstrate the adaptability and applicability of the developed operators.