This study outlines the local fractional integro-differential equations carried out by the local fractional calculus. The analytical solutions within local fractional Volterra and Abel’s integral equations via the Yang-Laplace transform are discussed. Some illustrative examples will be discussed. The obtained results show the simplicity and efficiency of the present technique with application t...

In this paper, some new Gronwall-Bellman type discrete fractional difference inequalities and fractional sum inequalities are established. Based on the theory of discrete fractional calculus, explicit bounds for unknown functions concerned are presented. These inequalities can be used as a handy tool in the qualitative analysis of solutions of discrete fractional difference equations. As for ap...

We introduce a discrete-time fractional calculus of variations on the time scale hZ, h > 0. First and second order necessary optimality conditions are established. Examples illustrating the use of the new Euler-Lagrange and Legendre type conditions are given. They show that solutions to the considered fractional problems become the classical discrete-time solutions when the fractional order of ...

Abstract By means of ς fractional sum operator, certain discrete nonlinear inequalities are replicated in this text. Considering the methodology calculus, we establish estimations Gronwall type for unknown functions. These a new form comparative with current writing discoveries up until point and can be viewed as supportive strategy to assess solutions partial differential equations numerically...

We begin with an introduction to a calculus of fractional finite differences. We extend the discrete Laplace transform to develop a discrete transform method. We define a family of finite fractional difference equations and employ the transform method to obtain solutions. AMS subject classification: 39A12, 26A33.

We define a class of discrete operators that, in particular, include the delta and nabla fractional operators. Moreover, we prove fundamental theorem calculus for these

This paper is devoted to the study of discrete fractional calculus; the particular goal is to define and solve well-defined discrete fractional difference equations. For this purpose we first carefully develop the commutativity properties of the fractional sum and the fractional difference operators. Then a ν-th (0 < ν ≤ 1) order fractional difference equation is defined. A nonlinear problem wi...