On conformable fractional calculus

Abstract

Recently, the authors Khalil, R., Al Horani, M., Yousef. A. and Sababheh, M., in " A new Denition Of Fractional Derivative, J. Comput. Appl. Math. 264. pp. 6570, 2014. " introduced a new simple well-behaved definition of the fractional derivative called conformable fractional derivative. In this article we proceed on to develop the definitions there and set the basic concepts in this new simple interesting fractional calculus. The fractional versions of chain rule, exponential functions, Gronwall's inequality, integration by parts, Taylor power series expansions, Laplace transforms and linear differential systems are proposed and discussed.

Conformable fractional Hermite-Hadamard inequalities via preinvex functions

“…Abdeljawad [1] have given the definition of left and right conformable fractional integrals of any order α > 0 as:…”

On the Solution of Burgers’ Equation with the New Fractional Derivative

“…For instance T. Abdel-jawad [5] provide fractional versions of the chain rule, exponential functions, Gronwall's inequality, integration by parts, Taylor power series expansions and Laplace transforms. N. Benkhettoua et al [6] introduced conformable time-scale fractional calculus.…”

Generalization of Hermite-Hadamard Type Inequalities via Conformable Fractional Integrals

“…Recently, the conformable integrals and derivatives have attracted the attention of many researchers, and many remarkable properties and inequalities for the conformable integrals and derivatives can be found in the literature [17][18][19][20][21][22][23][24]. Anderson [14] found the conformable integral version of the Hermite-Hadamard inequality as follows.…”