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 paper, we study the variable-order (VO) time-fractional diffusion equations. For a VO function $$\alpha (t)\in (0,1)$$ , develop an exponential-sum-approximation (ESA) technique to approach Caputo fractional derivative. The ESA keeps both quadrature exponents and number of exponentials in summation unchanged at different time level. Approximating parameters are properly selected achieve...

<span lang="EN-US">Fractional differential equations play a major role in expressing mathematically the real-world problems as they help attain good fit to experimental data. It is also known that fractional order controllers are more flexible than integer controllers. But when it comes numerical approximation of functions inaccuracies arise if conversion technique not chosen properly. So...

An efficient and accurate analytical solution is provided using the homotopy-Pade technique for the nonlinear vibration of parametrically excited cantilever beams. The model is based on the Euler-Bernoulli assumption and includes third order nonlinear terms arisen from the inertial and curvature nonlinearities. The Galerkin’s method is used to convert the equation of motion to a nonlinear ordin...

in this paper, a reliable approach is introduced to approximate periodic solutions of a system of coupled integrable dispersionless. the system is firstly, transformed into an ordinary differential equation by wave transformation. the solution of ode is obtained by the homotopy perturbation method. to show the periodic behavior of the solution, a modification based on the laplace transforms and...

In this paper, we propose a new object classification technique based on polygonal approximation of the open profile of object. The vertices of polygonal approximation are formed by high curvature points of the profile and they are selected by Fourier transform of the object contour. A series of features are computed from the polygonal approximation and then the minimum distance classifier is u...

We describe a general technique for estimating the intractable quantities that occur in a wide variety of largescale probabilistic models. The technique transforms intractable sums into integrals which are subsequently approximated via saddle point methods. When applied to sigmoid and noisy-OR networks, the technique yields a generic mean-field approximation as well as a second order Gaussian a...