Fractional logistic models in the frame of fractional operators generated by conformable derivatives

Analysis of some generalized ABC – Fractional logistic models

“…Let y 0 be an equilibrium point of the system (25), that is f (y) = 0, and assume that x(t) = y 0 + α(t). Since the ABC fractional derivative of the constant function is zero, following the same as in Section 4 in [27], we deduce that the system (25) has the following corresponding perturbed system:…”

Criteria of limit‐point case for conformable fractional Sturm‐Liouville operators

“…For recent results on conformable fractional calculus and the corresponding Sturm-Liouville equations, we refer the readers to Anderson and Ulness, 16 Al-Horani et al, 17 Al-Rifae and Abdeljawad, 18 Allahverdiev et al, 19 and Jarad et al 20 The papers of Abdeljawad et al 21 and Bas and Acay 22 are major in the Lyapunov inequalities for conformable boundary value problems. We note that there are other definitions such as the nonlocal fractional conformable derivatives generated by the local conformable ones given in Jarad et al 20 and Abdeljawad et al 23 In this paper, we consider the following 2 -order conformable fractional Sturm-Liouville operator:…”

Modeling, discretization, and hyperchaos detection of conformable derivative approach to a financial system with market confidence and ethics risk

“…Although Riemann-Liouville, Caputo, and Grunwald-Letnikov fractional derivatives [21][22][23][24][25][26][27][28] are widely used in physics, mathematics, medicine, economics, and engineering as shown above, these derivative definitions lack some of the agreed properties for classical differential operator, such as the chain rule. The conformable derivative can be regarded as a natural extension of the classical differential operator, which satisfies most important properties, such as the chain rule [29][30][31]. Researchers have recently applied conformable derivatives to many scientific fields [32][33][34][35][36][37][38][39][40][41][42].…”