Langevin Fractional System Driven by Two $\psi$-Caputo Derivatives with Random Effects
DOI:
https://doi.org/10.29020/nybg.ejpam.v18i1.5605Keywords:
Langevin equation, $\psi$-Caputo derivative, random variable, vector-valued norm, measure of noncompactnessAbstract
A nonlinear Langevin fractional system involving two $\psi$-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.
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Copyright (c) 2025 Mohamed Ziane, Hussein Al-Taani, Mohammad Ali Abudayah, Oualid Zentar, Ma’mon Abu Hammad
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