Fractional Langevin equations involving \(\psi\)-Caputo type in a Banach space: a solution sets approach

Oualid Zentar; Mohamed Ziane; Mohammed Al Horani

doi:10.24193/subbmath.2026.2.07

Authors

Oualid Zentar Department of Mathematics, University of Tiaret, Tiaret, Algeria https://orcid.org/0009-0004-3978-1243
Mohamed Ziane Department of Mathematics, University of Tiaret, Tiaret, Algeria; Laboratory of Research in Artificial Intelligence and Systems (LRAIS), University of Tiaret, Algeria https://orcid.org/0000-0002-9761-1128
Mohammed Al Horani Department of Mathematics, The University of Jordan, Amman, Jordan https://orcid.org/0000-0003-4853-6616

DOI:

https://doi.org/10.24193/subbmath.2026.2.07

Abstract

This paper investigates certain topological properties of the set of all global solutions for a class of nonlinear \(\psi\)-Caputo fractional Langevin equations. The nonlinearity, defined on an infinite-dimensional Banach space, is assumed to satisfy Nagumo-type growth conditions. An Aronszajn-type result is established using the nonlinear alternative for condensing operators, combined with the Browder–Gupta method. An illustrative example is provided to support the theoretical findings.

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