Abstract
In this paper, interval oscillation criteria for the nonlinear damped dynamic equations with forcing terms on time scales within conformable fractional derivatives are established. Our approach is determined from the implementation of generalized Riccati transformation, some properties of conformable time-scale fractional calculus, and certain mathematical inequalities. Also, we extend the study of oscillation to conformable fractional Euler-type dynamic equation. Examples are presented to emphasize the validity of the main theorems\enleadertwodots.
Highlights
Oscillation of Nonlinear Fractional Dynamic Equations with Forcing TermInterval oscillation criteria for the nonlinear damped dynamic equations with forcing terms on time scales within conformable fractional derivatives are established
In this paper, interval oscillation criteria for the nonlinear damped dynamic equations with forcing terms on time scales within conformable fractional derivatives are established
We extend the study of oscillation to conformable fractional Euler-type dynamic equation
Summary
Interval oscillation criteria for the nonlinear damped dynamic equations with forcing terms on time scales within conformable fractional derivatives are established. E theory of time scales was presented by Hilger [1] to unify the discrete and continuous analysis. It unifies the continuous and discrete cases and gives new areas in between such as q-calculus [2]. The importance has been given to fractional order calculus rather than integer order due to its applications in engineering such as neural networks, electrical and mechanical engineering, and population dynamics. In [19], Feng and Meng established the asymptotic and oscillatory behavior of the following dynamic equation of fractional order on time scales using the generalized Riccati transformation technique:. Alzabut et al [17] considered the following nonlinear damped dynamic equation with a conformable fractional derivative:
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