Existence, Stability and Controllability Results of Coupled Fractional Dynamical System on Time Scales

Existence, uniqueness, and controllability for Hilfer differential equations on times scales

“…Indeed, evaluating the supremum, for t ∈ [0, 1] of both sides of ( 19), and using the definition of the norm in the weighted space, we have (20). If L (𝜓(1)−𝜓(0)) 𝛼 g T (𝛾−1,1−𝛾)Γ(𝛼+1) < 1, then this will be a contraction map and we obtain the desired existence and uniqueness of solution to problem (2).…”

“…Although a well consolidated area, there are, however, still numerous open problems and paths to be unraveled [14][15][16][17]. A research path that some mathematicians have recently been interested consists to investigate fractional calculus on time scales [18][19][20][21][22].…”

Stability and controllability of nonautonomous neutral system with two delays

“…A dynamical system may exhibit a qualitative property known as controllability, which steers the system from an arbitrary initial state to an arbitrary final state under the set of admissible controls [19][20][21][22][23][24][25][26]. Controllability can be classified into two categories, that is, exact controllability and approximate controllability.…”

A robust computational framework for analyzing fractional dynamical systems

“…Here are some examples of the latest works. Malik and Kumar in [33] established existence, uniqueness, Hyer-Ulam stability and controllability results for a coupled fractional dynamical system on time scales. Heydari et al in [17] proposed a computational approach based on the shifted second-kind Chebyshev cardinal functions for obtaining an approximate solution of coupled variable order time-fractional sine-Gordon equations where the variableorder fractional operators are defined in the Caputo sense.…”