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

This paper presents a new framework of pseudo‐–fractional calculus in generalized Banach spaces by bringing together pseudo‐analysis, –calculus, and quantum calculus. We introduce Liouville–Caputo and Riemann–Liouville pseudo‐–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‐–fractional differential system, extending classical fractional and –fractional theories.