The dynamic response of an initially flat viscoelastic membrane is investigated. The viscoelastic model is described with fractional order derivatives. The membrane is subjected to surface transverse and inplane dynamic loads. The governing equations are three coupled second order nonlinear partial FDEs (fractional differential equations) of hyperbolic type in terms of the displacement componen...

The mathematical model of the distribution of deformation-relaxation and heat-mass fields in capillary-porous materials with fractal structure in the process of drying wood is regarded in the article. We used differential equations in partial derivatives of fractional order in description of this model. To describe the creep of wood fractional exponential Rabotnov’s function was used. The numer...

In this paper we propose an algorithm for the numerical solution of arbitrary differential equations of fractional order. The algorithm is obtained by using the following decomposition of the differential equation into a system of differential equation of integer order connected with inverse forms of Abel-integral equations. The algorithm is used for solution of the linear and non-linear equati...

In this paper we introduce higher order numerical methods for solving fractional differential equations. We use two approaches to this problem. The first approach is based on a direct discretisation of the fractional differential operator: we obtain a numerical method for solving a linear fractional differential equation with order 0 < α < 1. The order of convergence of the numerical method is ...

in this paper, we study a coupled system of nonlinear fractional differential equations with multi-point boundary condi- tions. the differential operator is taken in the riemann-liouville sense. applying the schauder fixed-point theorem and the contrac- tion mapping principle, two existence results are obtained for the following system d^{alpha}_{0+}x(t)=fleft(t,y(t),d^{p}_{0+}y(t)right), t in (0,...

In this paper we present the methods of Quasilinearization and Generalized Quasilinearization for hybrid Caputo fractional differential equations which are Caputo fractional differential equations with fixed moments of impulse. In order to prove this results we use the weakened assumption of -continuity in place of local Hölder continuity.

In this article, we implement a relatively new analytical technique, the reproducing kernel Hilbert space method (RKHSM), for solving integro-differential equations of fractional order. The solution obtained by using the method takes the form of a convergent series with easily computable components. Two numerical examples are studied to demonstrate the accuracy of the present method. The presen...

In this article, the modified simple equation method has been extended to celebrate the exact solutions of nonlinear partial time-space differential equations of fractional order. Firstly, the fractional complex transformation has been implemented to convert nonlinear partial fractional differential equations into nonlinear ordinary differential equations. Afterwards, modified simple equation m...

In this article, the second kind Chebyshev wavelet method is presented for solving a class of multi-order fractional differential equations (FDEs) with variable coefficients. We first construct the second kind Chebyshev wavelet, prove its convergence and then derive the operational matrix of fractional integration of the second kind Chebyshev wavelet. The operational matrix of fractional integr...