Pseudo-Quantum Fractional Calculus and Existence of Solutions for Delay Pseudo-Fractional Differential Equations in Generalized Banach Spaces

Alireza Hatami, Reza Saadati, Mohammad Bagher Ghaemi and Donal O’Regan

Journal of Mathematics, 2026, vol. 2026, 1-15

Abstract: This paper presents a new framework of pseudo-q–fractional calculus in generalized Banach spaces by bringing together pseudo-analysis, G–calculus, and quantum calculus. We introduce Liouville–Caputo and Riemann–Liouville pseudo-q–fractional operators and outline their main properties. Then, by applying the Banach fixed point principle, we establish the existence and uniqueness of solutions for a pseudo-q–fractional differential system, extending classical fractional and q–fractional theories.

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:4287317

DOI: 10.1155/jom/4287317

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