On Fractional Sturm–Liouville Problem With Prabhakar Fractional Derivative

Source abstract

ABSTRACT In this study, we introduce a self‐adjoint fractional Sturm–Liouville problem involving Prabhakar fractional derivative, resulting in a unified framework that encompasses Riemann–Liouville and classical settings. By establishing integration‐by‐part identities for Prabhakar derivative, we demonstrate the essential spectral properties of the fractional Prabhakar Sturm–Liouville problem, including orthogonality of eigenfunctions. Further, the problem's well‐posedness is studied by proving coercivity and boundedness properties.