A fractal-fractional gingerbread-man map generalized by p−fractal-fractional difference operator

Authors

DOI:

https://doi.org/10.31489/2025m2/76-92

Keywords:

fractional calculus, fractal calculus, fractional difference operator, fractal-fractional differential operator, fractal-fractional calculus, fractal-fractional discrete operator

Abstract

By using the generalization of the gamma function (p−gamma function: Γp(.)), we introduce a generalization of the fractal-fractional calculus which is called p−fractal-fractional calculus. Examples are illustrated including the basic power functions. As applications, we formulate the p−fractal-fractional difference operators. A class of maps, called gingerbread-man maps, is investigated. We present a new idea of a stability for continuous system, based on three parameters. Sufficient conditions are illustrated to obtain the stability of the system.

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Published

2025-06-30

How to Cite

Ibrahim, R., & Momani, S. (2025). A fractal-fractional gingerbread-man map generalized by p−fractal-fractional difference operator. Bulletin of the Karaganda University. Mathematics Series, 118(2), 76–92. https://doi.org/10.31489/2025m2/76-92

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Section

MATHEMATICS