the aim of this paper is to design a fractional order sliding mode controllers (fosmc)for a class of dc-dc converters such as boost and buck converters. firstly, the control lawis designed with respect to the properties of fractional calculus, the design yields an equiv-alent control term with an addition of discontinuous (attractive) control law. secondly, themathematical proof of the stabilit...

This paper establishes some closed formulas for RiemannLiouville impulsive fractional integral calculus and also for RiemannLiouville and Caputo impulsive fractional derivatives. Keywords—RimannLiouville fractional calculus, Caputo fractional derivative, Dirac delta, Distributional derivatives, Highorder distributional derivatives.

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 aim of this paper is to present a new numerical method for solving the bagley-torvik equation. this equation has an important role in fractional calculus. the fractional derivatives are described based on the caputo sense. some properties of the sinc functions required for our subsequentdevelopment are given and are utilized to reduce the computation of solution of the bagley-torvik equatio...

‎‎in this paper‎, ‎the existence and uniqueness of positive solutions for a class of nonlinear initial value problem for a finite fractional difference equation obtained by constructing the upper and lower control functions of nonlinear term without any monotone requirement‎ .‎the solutions of fractional difference equation are the size of tumor in model tumor growth described by the gompertz f...

A special function is a that typically entitled after an early scientist who studied its features and has specific application in mathematical physics or another area of mathematics. There are few significant examples, including the hypergeometric unique species. These types functions generalized by fractional calculus, fractal, q-calculus, (q,p)-calculus k-calculus. By engaging notion q-fracti...

This paper provides a formalized basis for initialization in the fractional calculus. The intent is to make the fractional calculus readily accessible to engineering and the sciences. A modified set of definitions for the fractional calculus is provided which formally include the effects of initialization. Conceptualizations of fractional derivatives and integrals are shown. Physical examples o...

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...

In this work, we extend the existing local fractional Sumudu decomposition method to solve the nonlinear local fractional partial differential equations. Then, we apply this new algorithm to resolve the nonlinear local fractional gas dynamics equation and nonlinear local fractional Klein-Gordon equation, so we get the desired non-differentiable exact solutions. The steps to solve the examples a...

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 ...