Langevin Fractional System Driven by Two $ψ$-Caputo Derivatives with Random Effects (European Journal of Pure and Applied Mathematics, 2025)
A nonlinear Langevin fractional system involving two $ψ$-Caputo derivatives with random effects is investigated. First, a random version of Perov's fixed-point theorem in generalized Banach space endowed with the Bielecki-type vector-valued norm is employed to achieve a uniqueness result. Second, the existence result is established using Sadovskii's fixed point principle under fairly general conditions on the nonlinear forcing terms. Finally, our findings are justified through illustrative examples.
Keywords: Langevin equation, $ψ$-Caputo derivative, random variable, vector-valued norm, measure of noncompactness