Oscillation of differential equations in the frame of nonlocal fractional derivatives generated by conformable derivatives

Abstract

Recently, Jarad et al. in (Adv. Differ. Equ. 2017:247, 2017) defined a new class of nonlocal generalized fractional derivatives, called conformable fractional derivatives (CFDs), based on conformable derivatives. In this paper, sufficient conditions are established for the oscillation of solutions of generalized fractional differential equations of the formRe(α) ≥ 0 in the Riemann-Liouville setting and a I α,ρ is the left-fractional conformable integral operator. The results are also obtained for CFDs in the Caputo setting. Examples are provided to demonstrate the effectiveness of the main result.

Determination of supercapacitor parameters based on fractional differential equations

“…This fractional conformable derivative has been applied for modeling problems in different fields such as science, technology, and engineering with excellent results. ()…”

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

“…The function h 3 (t) = (ta) ρ-ρj is decreasing for j > 1 and ρ > 0. Thus, for t ≥ T 1 , we have (see [21])…”

“…The oscillation theory for fractional differential and difference equations has been studied by some authors (see [19][20][21][22][23][24][25][26][27][28][29]). In [23] the authors studied the oscillation theory for fractional differential equations by considering fractional initial value problem of the form Recently, in [21] the authors studied the oscillation of a conformable initial value problem of the form ⎧ ⎨ ⎩ a D α,ρ x(t) + f 1 (t, x) = r(t) + f 2 (t, x), t > a, lim t→a + a J j-α,ρ x(t) = b j (j = 1, 2, . .…”

Oscillation theorems for three classes of conformable fractional differential equations

“…This new theory is improved by Abdeljawad [13]. For recent results on conformable fractional derivatives, we refer the reader to [14][15][16][17][18][19][20][21][22][23]. This new definition satisfies formulas of the derivatives of the product and quotient of two functions and has a simpler chain rule.…”