Analysis of the local Drude model involving the generalized fractional derivative

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

“…II. We note that many aspects of new class CFD definitions and the generalized conformable fractional operators have been discussed in other studies, [9][10][11][12][13][14][15][16][17][18]22 and some of them can be extended to operators proposed here. Further research is necessary to develop analytical and numerical schemes for these operators.…”

“…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.…”

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 efficient methods for solving fractional Lane–Emden equations with conformable fractional derivative

“…This definition is very simple and more welcome than other fractional definitions since it has been receiving a lot of attention, many applications and phenomena can be modeled based on the CFDs, and it contains many interesting advantages such as the following: it is a local derivative that simulates the normal derivative because it depends on the limit in its formulation and it generalizes all concepts of ordinary calculus and can solve different fractional differential equations with all cases. In addition to this definition, there is another type of local derivatives called non-conformable fractional derivative, and for this purpose, the authors point out the publications [17][18][19][20][21][22]. In recent years, many authors have handled and studied the Lane-Emden equations because they were used to formulate lots of phenomena in physics and astrophysics [23][24][25][26][27][28].…”