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13 papers found.
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Computational Optimization of Residual Power Series Algorithm for Certain Classes of Fuzzy Fractional Differential Equations

This paper aims to present a novel optimization technique, the residual power series (RPS), for handling certain classes of fuzzy fractional differential equations of order under strongly generalized differentiability. The proposed technique relies on generalized Taylor formula under Caputo sense aiming at extracting a supportive analytical solution in convergent series form. The...

Solutions to Uncertain Volterra Integral Equations by Fitted Reproducing Kernel Hilbert Space Method

We present an efficient modern strategy for solving some well-known classes of uncertain integral equations arising in engineering and physics fields. The solution methodology is based on generating an orthogonal basis upon the obtained kernel function in the Hilbert space in order to formulate the analytical solutions in a rapidly convergent series form in terms of their -cut...

Toward the Approximate Solution for Fractional Order Nonlinear Mixed Derivative and Nonlocal Boundary Value Problems

The paper is devoted to the study of operational matrix method for approximating solution for nonlinear coupled system fractional differential equations. The main aim of this paper is to approximate solution for the problem under two different types of boundary conditions, -point nonlocal boundary conditions and mixed derivative boundary conditions. We develop some new...

Toward the Approximate Solution for Fractional Order Nonlinear Mixed Derivative and Nonlocal Boundary Value Problems

The paper is devoted to the study of operational matrix method for approximating solution for nonlinear coupled system fractional differential equations. The main aim of this paper is to approximate solution for the problem under two different types of boundary conditions, -point nonlocal boundary conditions and mixed derivative boundary conditions. We develop some new...

A Novel Representation of the Exact Solution for Differential Algebraic Equations System Using Residual Power-Series Method

We implement a relatively new analytic iterative technique to get approximate solutions of differential algebraic equations system based on generalized Taylor series formula. The solution methodology is based on generating the residual power series expansion solution in the form of a rapidly convergent series with easily computable components. The residual power series method...

Iterative Reproducing Kernel Method for Solving Second-Order Integrodifferential Equations of Fredholm Type

April 2014; Published 27 April 2014 Academic Editor: Alberto Cabada Copyright © 2014 Iryna Komashynska and Mohammed AL-Smadi. This is an open access article distributed under the Creative Commons

Iterative Reproducing Kernel Method for Solving Second-Order Integrodifferential Equations of Fredholm Type

April 2014; Published 27 April 2014 Academic Editor: Alberto Cabada Copyright © 2014 Iryna Komashynska and Mohammed AL-Smadi. This is an open access article distributed under the Creative Commons

Iterative Reproducing Kernel Method for Solving Second-Order Integrodifferential Equations of Fredholm Type

April 2014; Published 27 April 2014 Academic Editor: Alberto Cabada Copyright © 2014 Iryna Komashynska and Mohammed AL-Smadi. This is an open access article distributed under the Creative Commons

Analytical Study of Fractional-Order Multiple Chaotic FitzHugh-Nagumo Neurons Model Using Multistep Generalized Differential Transform Method

The multistep generalized differential transform method is applied to solve the fractional-order multiple chaotic FitzHugh-Nagumo (FHN) neurons model. The algorithm is illustrated by studying the dynamics of three coupled chaotic FHN neurons equations with different gap junctions under external electrical stimulation. The fractional derivatives are described in the Caputo sense...

A Numerical Iterative Method for Solving Systems of First-Order Periodic Boundary Value Problems

2014 Academic Editor: Hak-Keung Lam Copyright © 2014 Mohammed AL-Smadi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use

A Numerical Iterative Method for Solving Systems of First-Order Periodic Boundary Value Problems

2014 Academic Editor: Hak-Keung Lam Copyright © 2014 Mohammed AL-Smadi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use

A Computational Method for Two-Point Boundary Value Problems of Fourth-Order Mixed Integrodifferential Equations

27 July 2012; Accepted 29 January 2013 Academic Editor: Hung Nguyen-Xuan Copyright © 2013 Mohammed Al-Smadi et al. This is an open access article distributed under the Creative Commons Attribution

Application of Reproducing Kernel Method for Solving Nonlinear Fredholm-Volterra Integrodifferential Equations

This paper investigates the numerical solution of nonlinear Fredholm-Volterra integro-differential equations using reproducing kernel Hilbert space method. The solution ?(?) is represented in the form of series in the reproducing kernel space. In the mean time, the n-term approximate solution ??(?) is obtained and it is proved to converge to the exact solution ?(?). Furthermore...