Fractional Langevin equations involving ψ-Caputo type in a Banach space: a solution sets approach
DOI:
https://doi.org/10.24193/subbmath.2026.2.07Keywords:
Fractional Langevin equations, ψ-Caputo derivative, measure of non compactness, Aronszajn-type propertyAbstract
This paper investigates certain topological properties of the set of all global solutions for a class of nonlinear ψ-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.
Mathematics Subject Classification (2010): 34A08, 47H08, 34G20.
Received 07 September 2025; Accepted 24 March 2026.
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