What question did this study set out to answer?

The aim is to develop a pseudo-fractional calculus framework in generalized Banach spaces and establish solution existence for delay differential equations.

June 2, 2026Open Access

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

Key Points

The aim is to develop a pseudo-fractional calculus framework in generalized Banach spaces and establish solution existence for delay differential equations.
Introduced Liouville-Caputo and Riemann-Liouville pseudo-fractional operators.
Applied the Banach fixed point principle to explore solutions for pseudo-fractional differential systems.
Demonstrated the existence and uniqueness of solutions for the pseudo-fractional differential system.

Abstract

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.

Read Full Paperexternally

Bookmark

View Full Paper

Cite This Study

Hatami et al. (Thu,) studied this question.

synapsesocial.com/papers/6a1e734530b38c64201b683a https://doi.org/https://doi.org/10.1155/jom/4287317

Bookmark

View Full Paper