On a Partial Fractional Hybrid Version of Generalized Sturm–Liouville–Langevin Equation

As we know one of the most important equations which have many applications in various areas physics, mathematics, and financial markets, is Sturm–Liouville equation. In this paper, by using α-ψ-contraction technique fixed point theory employing some functional inequalities, study existence solutions partial fractional hybrid case generalized Sturm–Liouville-Langevin under boundary value conditions. Towards end, present two examples with numerical graphical simulation to illustrate our main results.