Fractional calculus; Conformable operators; Calculus on time scales Abstract A conformable time-scale fractional calculus of order a 2 0; 1 is introduced. The basic tools for fractional differentiation and fractional integration are then developed. The Hilger timescale calculus is obtained as a particular case, by choosing a 1⁄4 1. a 2015 The Authors. Production and hosting by Elsevier B.V. on ...

Exact solutions to conformable time fractional (3+1)dimensional equations are derived by using the modified form of the Kudryashov method. The compatible wave transformation reduces the equations to an ODE with integer orders. The predicted solution of the finite series of a rational exponential function is substituted into this ODE. The resultant polynomial equation is solved by using algebrai...

In this paper the more general comparison theorems for conformable fractional differential equations is proposed and tested. Thus we prove some inequalities for conformable integrals by using the generalization of Sturm’s separation and Sturm’s comparison theorems. The results presented here would provide generalizations of those given in earlier works. The numerical example is also presented t...

In the article, we establish several Ostrowski type inequalities involving the conformable fractional integrals. As applications, we find new inequalities for the arithmetic and generalized logarithmic means.

Conformable space-time fractional linear telegraph equations are examined using a new method known as conformable Elzaki decomposition method. The suggested combines the Adomian with transform. It is found that numerical simulations confirm effectiveness and reliability of proposed

In this paper we present an extension of Fractional Laplace Transform in the framework non-conformable local fractional derivative. Its main properties are studied and it is applied to resolution differential equations.