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 subsequent development are given and are utilized to reduce the computation of solution of the Bagley-Torvik equati...

Fractional calculus (differentiation and integration of arbitrary order) arise naturally in various areas of applied science and engineering such as mechanics, electricity, chemistry, biology, economics, control theory, signal and image processing, polymer rheology, regular variation in thermodynamics, biophysics, blood flow phenomena, aerodynamics, electro-dynamics of complex medium, viscoelas...

A new controller design method is proposed to synchronize the fractional-order hyperchaotic system through the stability theory of fractional calculus; the synchronization between two identical fractional-order Chen hyperchaotic systems is realized by designing only two suitable controllers in the response system. Furthermore, this control scheme can be used in secure communication via the tech...

Interest in studies on fractional calculus and its applications has greatly increased recent years. Fractional-order analysis the potential to enhance dynamic structure of chaotic systems. This study presents implementation a lower-order electronic circuit using standard components for Sprott K system. To our knowledge, there are no realizations literature where value fractional-order parameter...

This paper deals with the design fractional solution of Bessel equation. We obtain explicit solutions of the equation with the help of fractional calculus techniques. Using the N-fractional calculus operator N(ν) method, we derive the fractional solutions of the equation.

In this paper, we will study about Fractional-order partial differential equations in Mathematical Science and introduce analyse fractional calculus with an integral operator that contains the Caputo- Fabrizio’s fractional-order derivative. The advanced method is appropriate union of new transform named as ‘Mohand transform’ homotopy perturbation method. Some numerical examples are used to comm...

This research investigates the synchronization of distributed delayed discrete-time fractional-order complex-valued neural networks. The necessary conditions have been established for stability proposed networks using theory discrete fractional calculus, Laplace transform, and Mittag–Leffler functions. In order to guarantee global asymptotic stability, adequate criteria are determined Lyapunov’...

We develop efficient numerical methods for fractional order PDEs, and employ them to investigate viscoelastic constitutive laws for arterial wall mechanics. Recent simulations using one-dimensional models [1] have indicated that fractional order models may offer a more powerful alternative for modeling the arterial wall response, exhibiting reduced sensitivity to parametric uncertainties compar...

The aim of the present paper is to introduce and investigate a new subclass of Bazilevi'{c} functions in the punctured unit disk $mathcal{U}^*$ which have been described through using of the well-known fractional $q$-calculus operators, Hadamard product and a linear operator. In addition, we obtain some sufficient conditions for the func...