Deepa Gupta

most citedStability and Bifurcation Analysis of Two-Term Fractional Differential Equation with Delay

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math.DS2024

Analysis of Stability, Bifurcation, and Chaos in Generalized Mackey-Glass Equations

Deepa Gupta, Sachin Bhalekar

Mackey-Glass equation arises in the leukemia model. We generalize this equation to include fractional-order derivatives in two directions. The first generalization contains one whe…

math.DS2024★ 1 cited

Stability and Bifurcation Analysis of Two-Term Fractional Differential Equation with Delay

Sachin Bhalekar, Deepa Gupta

This manuscript deals with the stability and bifurcation analysis of the equation $D^{2 α} x (t) + c D^{α} x (t) = a x (t) + b x (t - τ)$ , where $0 < α < 1$ and $τ > 0$ . We sketch the boundaries of vario…

math.DS2024★ 1 cited

Fractional Order Sunflower Equation: Stability, Bifurcation and Chaos

Deepa Gupta, Sachin Bhalekar

The sunflower equation describes the motion of the tip of a plant due to the auxin transportation under the influence of gravity. This work proposes the fractional-order generaliza…

math.DS2022

Can a Fractional Order Delay Differential Equation be Chaotic Whose Integer-Order Counterpart is Stable?

Sachin Bhalekar, Deepa Gupta

For the fractional order systems \[D^αx(t)=f(x),\quad 0<α\leq 1,\] one can have a critical value of $α$ viz $α_{*}$ such that the system is stable for $0 < α < α_{*}$ and unstable for $α_*…

math.DS2022

Stability and Bifurcation Analysis of a Fractional Order Delay Differential Equation Involving Cubic Nonlinearity

Sachin Bhalekar, Deepa Gupta

Fractional derivative and delay are important tools in modeling memory properties in the natural system. This work deals with the stability analysis of a fractional order delay dif…