This article presents a rigorous review of the conformable fractional derivative given by J. E. Napoles in [11], studying its classical properties, as differential operator. Likewise, applications are to Physics, specifically free fall bodies and Newton’s law cooling.

The objective of this article is to develop some results on conformable fractional derivatives, specifically the one known as Khalil's derivative. Its origin, properties, comparisons with other derivatives and applications population grow Newton law cooling models are studied.

Abstract In this paper, Sobolev-type conformable fractional stochastic evolution inclusions with Clarke subdifferential and nonlocal conditions are studied. By using calculus, analysis, properties of nonsmooth sufficient for controllability the considered problem established. Finally, an example is given to illustrate obtained results.

Abstract The fundamental objective of this article is to investigate about the boundary value problem with uses a generalized conformable fractional derivative introduced by Zarikaya et al. ( On calculus , TWMS J. App. Eng. Math. 9 (2019), no. 4, 792–799, http://jaem.isikun.edu.tr/web/images/articles/vol.9.no.4/11.pdf ). In development article, using classical methods calculus, we find definiti...

This paper intends to obtain accurate and convergent numerical solutions of linear space-time matching telegraph fractional equations by means a double Sumudu transformation method. Moreover, the model is equipped explain work, accuracy sobriety in its presentation method, as result, proposed method shows an effective convenient way, employ proven problems science engineering.

The advancements of integral inequalities with the help fractional operators have recently been focus attention in theory inequalities. In this study, we first review some fundamental concepts, and then using \(k\)-conformable integrals, establish a new identity for differentiable functions. Then, considering as an auxiliary result, several Ostrowski-type are presented functions whose modulus d...

The goal of this work is to introduce the two-parameter conformable fractional semigroups and provide a definition its infinitesimal generator. For such generators, we develop multiple results. In addition, show that solution for abstract Cauchy problems.

This work proposes a valuable and successful strategy for approximating the solutions to Bagley–Torvik system, which plays an essential role in fractional calculus. The Caputo sense is used derive basic conformable fractional. problem numerically solved this study using effective symmetric projection method. From symmetry, there are some interesting original results. proposed approach has two k...