Displaying similar documents to “Numerical solutions to integral equations equivalent to differential equations with fractional time”

An operational Haar wavelet method for solving fractional Volterra integral equations

Habibollah Saeedi, Nasibeh Mollahasani, Mahmoud Mohseni Moghadam, Gennady N. Chuev (2011)

International Journal of Applied Mathematics and Computer Science

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A Haar wavelet operational matrix is applied to fractional integration, which has not been undertaken before. The Haar wavelet approximating method is used to reduce the fractional Volterra and Abel integral equations to a system of algebraic equations. A global error bound is estimated and some numerical examples with smooth, nonsmooth, and singular solutions are considered to demonstrate the validity and applicability of the developed method.

Solving Fractional Diffusion-Wave Equations Using a New Iterative Method

Daftardar-Gejji, Varsha, Bhalekar, Sachin (2008)

Fractional Calculus and Applied Analysis

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Mathematics Subject Classification: 26A33, 31B10 In the present paper a New Iterative Method [1] has been employed to find solutions of linear and non-linear fractional diffusion-wave equations. Illustrative examples are solved to demonstrate the efficiency of the method. * This work has partially been supported by the grant F. No. 31-82/2005(SR) from the University Grants Commission, N. Delhi, India.

Optimal approximation simulation and analog realization of the fundamental fractional order transfer function

Abdelbaki Djouambi, Abdelfatah Charef, Alina Voda besancon (2007)

International Journal of Applied Mathematics and Computer Science

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This paper provides an optimal approximation of the fundamental linear fractional order transfer function using a distribution of the relaxation time function. Simple methods, useful in systems and control theories, which can be used to approximate the irrational transfer function of a class of fractional systems fora given frequency band by a rational function are presented. The optimal parameters of the approximated model are obtained by minimizing simultaneously the gain and the phase...

On the numerical solutions of some fractional ordinary differential equations by fractional Adams-Bashforth-Moulton method

Haci Mehmet Baskonus, Hasan Bulut (2015)

Open Mathematics

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In this paper, we apply the Fractional Adams-Bashforth-Moulton Method for obtaining the numerical solutions of some linear and nonlinear fractional ordinary differential equations. Then, we construct a table including numerical results for both fractional differential equations. Then, we draw two dimensional surfaces of numerical solutions and analytical solutions by considering the suitable values of parameters. Finally, we use the L2 nodal norm and L∞ maximum nodal norm to evaluate...

Convergence of the matrix transformation method for the finite difference approximation of fractional order diffusion problems

Béla J. Szekeres, Ferenc Izsák (2017)

Applications of Mathematics

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Numerical solution of fractional order diffusion problems with homogeneous Dirichlet boundary conditions is investigated on a square domain. An appropriate extension is applied to have a well-posed problem on ℝ 2 and the solution on the square is regarded as a localization. For the numerical approximation a finite difference method is applied combined with the matrix transformation method. Here the discrete fractional Laplacian is approximated with a matrix power instead of computing the...