In this work, a non-integer order Airy equation involving Liouville differential operator is considered. Proposing an undetermined integral solution to the left fractional Airy differential equation, we utilize some basic fractional calculus tools to clarify the closed form. A similar suggestion to the right FADE, converts it into an equation in the Laplace domain. An illustration t...

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...

The theory of derivatives and integrals of fractional in fractional calculus have found enormousapplications in mathematics, physics and engineering so for that reason we need an efficient and accurate computational method for the solution of fractional differential equations. This paper presents a numerical method for solving a class of linear and nonlinear multi-order fractional differential ...

fractional calculus has been used to model the physical and engineering processes that have found to be best described by fractional differential equations. for that reason, we need a reliable and efficient technique for the solution of fractional differential equations. the aim of this paper is to present an analytical approximation solution for linear and nonlinear multi-order fractional diff...

The main aim of this contribution is to introduce the fundamentals of the Fractional Order Calculus (FOC) and outline its possible application to analysis and synthesis of control systems. The basic theoretical concepts of FOC are followed by techniques for potential fractional order systems description and stability investigation. Moreover, the paper offers the overview of the existing fractio...

Several approaches to the formulation of a fractional theory calculus "variable order" have appeared in literature over years. Unfortunately, most these proposals lack rigorous mathematical framework. We consider an alternative view on problem, originally proposed by G. Scarpi early seventies, based naive modification representation Laplace domain standard kernels functions involved (constant-o...