Forced oscillation of fractional differential equations via conformable derivatives with damping term

Abstract

Based on the properties of nonlocal fractional calculus generated by conformable derivatives, we establish some sufficient conditions for oscillation of all solutions for fractional differential equations with damping term. Forced oscillation of conformable differential equations in the frame of Riemann, as well as of Caputo type, is established. Examples are provided to demonstrate the effectiveness of the main results.

Existence and oscillation results for the Hybrid generalized pantograph Hilfer fractional difference equation

“…In the past twenty years, researchers have been continuing this work due to the growth in the ideology of fractional calculus. For examples, see [2,8,39] and the references cited therein.…”

Controllability of higher-order fractional damped stochastic systems with distributed delay

“…A nonlinear dynamical system with fractional damping is of great importance in many fields such as engineering and applied sciences [2,30,32]. As a replacement for ordinary derivatives, the viscoelastic models containing fractional derivatives are novel research issues.…”

Final Value Problem for Parabolic Equation with Fractional Laplacian and Kirchhoff’s Term

“…Let us mention some recent works on diffusion equations with a conformable derivative, for example, [2,5,[7][8][9][10][11][12][13][14][15][16]. Some interesting papers on fractional diffusion equations can be found in [17][18][19][20][21][22][23][24] and the references therein.…”