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math.DS2026
Maps of q-deformed fractional order: From circle to cardioid via crescent
Sachin Bhalekar, Prashant M. Gade
We introduce a class of \(q\)-deformed fractional order maps by replacing the classical binomial memory kernel in discrete fractional dynamics with Gaussian (\(q\)-) binomial coeff…
math.DS2025
Analysis of the maps with variable fractional order
Prashant M. Gade, Sachin Bhalekar, Janardhan Chevala
Fractional order differential and difference equations are used to model systems with memory. Variable order fractional equations are proposed to model systems where the memory cha…
math.DS2024
Dynamical Analysis Of Fractional Order Generalized Logistic Map
Sachin Bhalekar, Janardhan Chevala, Prashant M. Gade
In this work, we propose a generalization to the classical logistic map. The generalized map preserves most properties of the classical map and has richer dynamics as it contains t…