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

Author

Listed:
  • Alireza Hatami
  • Reza Saadati
  • Mohammad Bagher Ghaemi
  • Donal O’Regan

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.

Suggested Citation

  • Alireza Hatami & Reza Saadati & Mohammad Bagher Ghaemi & Donal O’Regan, 2026. "Pseudo-Quantum Fractional Calculus and Existence of Solutions for Delay Pseudo-Fractional Differential Equations in Generalized Banach Spaces," Journal of Mathematics, Hindawi, vol. 2026, pages 1-15, May.
    • Handle: RePEc:hin:jjmath:4287317
    DOI: 10.1155/jom/4287317
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