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.
Highlights
Fractional differential equations gained considerable importance due to their various applications in viscoelasticity, electroanalytical chemistry, control theory, many physical problems, etc
The oscillation theory for fractional differential and difference equations has been studied by some authors
Where Daq denotes the Riemann–Liouville fractional derivative starting at a point a, of order q with 0 < q ≤ 1, Ja1–q is the Riemann–Liouville fractional integral starting at a point a, of order 1 – q, f1, f2 are continuous functions
Summary
Fractional differential equations gained considerable importance due to their various applications in viscoelasticity, electroanalytical chemistry, control theory, many physical problems, etc. In [23] the authors studied the oscillation theory for fractional differential equations by considering fractional initial value problem of the form In [21] the authors studied the oscillation of a conformable initial value problem of the form In [22] the authors studied forced oscillatory properties of solutions to the nonlinear fractional initial value problem with damping
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