On the conformable fractional logistic models

Abstract

In this paper, we use a conformable fractional derivative GTα, with kernel Tfalse(t,αfalse)=efalse(α−1false)t, in order to study the fractional differential equation associated to a logistic growth model. As a practical application, we estimate the order of the derivative of the fractional logistic models, by solving an inverse problem involving real data. In the same direction, we show the feasibility of our approach with respect to the Ordinary, Khalil et al and Caputo approaches.

Generalised conformable sliding mode control

“…On the other hand, conventional fractional derivatives lead to difficulties during numerical computations for modelling and control purposes. Consequently, novel tools have been investigated in order to generalise the conventional integro‐differential operators, but considering only local information of the process 4 . In this sense, R. Khalil et al proposed the conformable derivative, 5 which consists of a local operator that extends the classical derivative definition and, for a differentiable function, it may be seen as the product of the conventional derivative with a corresponding time varying function.…”

“…This operator brings extra degrees of freedom to design the kernel function. Some interesting applications of the concept of conformable derivative can be found in literature 11–18 …”

Note on the conformable boundary value problems: Sturm’s theorems and Green’s function

“…The difference between conformable fractional derivative and non-conformable fractional derivative is that the tangent line angle is conserved in the conformable one, while it is not conserved in the sense of nonconformable one [25] (see also [26,34,36,37] for more new related results about this newly proposed definition of non-conformable fractional derivative). The definition of non-conformable fractional derivative has been investigated and applied in various research studies and applications of physics and natural sciences such as the stability analysis, oscillatory character, and boundedness of fractional Liénard-type systems [27,28,33], analysis of the local fractional Drude model [29], Hermite-Hadamard inequalities [30], fractional Laplace transform [31], fractional logistic growth models [32], oscillatory character of fractional Emden-Fowler equation [35], asymptotic behavior of fractional nonlinear equations [38], and qualitative behavior of nonlinear differential equations [39]. This paper is organized as follows: In Sec.…”

Two classes of conformable fractional Sturm‐Liouville problems: Theory and applications

“…The authors of previous works 9- 14 introduced a new class of conformable and non-CFDs and studied their algebraic properties, see also other studies 15,16 for recent studies on generalized conformable fractional operators. More recently, Fleitas et al [17][18][19] presented a general definition of CFD and its operational properties and demonstrated its applications in solving the classical Drude model and the logistic growth model. Rosa et al 20 investigated the dual conformable derivative, definition, simple properties, and perspectives for applications.…”

“…Zhao et al established the multivariate theory of GCFD and illustrated the conformable Maxwell equations, and theorems for Conformable Gauss's, Green's, and Stokes's Theorem, see Zhao et al 22 Though, this new local fractional derivative fails some properties as pointed out in previous studies, [23][24][25][26] it seems to account for many deficiencies of some of the earlier proposed definitions which are of great importance in applied sciences and therefore suitable for more applications. Some authors followed this work and explored potential applications in various fields such as the control theory of dynamical systems, [27][28][29][30] mathematical biology and epidemiology, 19,[31][32][33][34] mechanics, 16,35,36 systems of linear and nonlinear conformable fractional differential equations (CFDEs), [37][38][39] quantum mechanics, 40,41 variational calculus, 42,43 arbitrary time scale problems, [44][45][46] modelling of diffusion, 47,48 stochastic process, 49,50 and optics. 51 Some analytical and numerical methods have attracted great interest and became an important tool for differential equations with CFDs, (see previous studies ).…”