S. Sivasundaram

TL;DR: Based on the stability analysis, the critical values of the fractional order for which Hopf bifurcations may occur are identified and Simulation results are presented to illustrate the theoretical findings and to show potential routes towards the onset of chaotic behavior when the fractions of the system increases.

TL;DR: In this paper, the existence results for a two-point boundary value problem involving nonlinear impulsive hybrid differential equation of fractional order q ∈ ( 1, 2 ] were discussed.

TL;DR: The existence and uniqueness of solutions for a four-point nonlocal boundary value problem of nonlinear integro-differential equations of fractional order q ∈ (1, 2] are proved by applying some standard fixed point theorems.

TL;DR: In this paper, it was shown that the limit cycle observed in numerical simulations of a simple fractional-order neural network cannot be an exact periodic solution of the system, in contrast with integer-order derivatives.

TL;DR: In this paper, the existence results for a boundary value problem of nonlinear impulsive differential equations of fractional-order q(1,2] with integral boundary conditions were proved by applying the contraction mapping principle and Krasnoselskii's fixed point theorem.