20 citations · 111 across the 35 of their papers we have counts for
36 papers
Pantograph Difference Equations: Stability, Multistability, and Chaos
Prashant M. Gade, Sachin Bhalekar
Pantograph equations are functional differential equations with proportional delay, typically involving terms of the form , where . These equations have been studied…
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…
Stability Analysis of Pantograph Delay Differential Equations
Sachin Bhalekar
This article investigates the stability of pantograph delay differential equations, in which the delayed argument is proportional to the present time. We derive analytic criteria t…
Stability and Bifurcation Analysis of Fractional Delay Differential Equation with a Delay-dependent Coefficient
Pragati Dutta, Sachin Bhalekar
This paper investigates the stability of different regions in the -plane for a class of fractional delay differential equations given by \begin{equation} D^α x(t) = -γx(t) +…
Analysis of Chaos and Bifurcation in Nonlinear two-delay differential equation
Pragati Dutta, Sachin Bhalekar
This paper studies how complicated and irregular behavior, known as chaos, can arise in a simple mathematical model that includes time delays. The model is a delay differential equ…
Stability Regions and Bifurcations for Higher-Order Fractional Difference Equations
Janardhan Chevala, Sachin Bhalekar
We study stability regions for the higher-order, two-term fractional difference equation , where , $a >…