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Ordinary Differential Equations and Applied Dynamics Commons™
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Articles 1 - 3 of 3
Full-Text Articles in Ordinary Differential Equations and Applied Dynamics
On The Convergence Of Two-Dimensional Fuzzy Volterra-Fredholm Integral Equations By Using Picard Method, Ali Ebadian, Foroozan Farahrooz, Amirahmad Khajehnasiri
On The Convergence Of Two-Dimensional Fuzzy Volterra-Fredholm Integral Equations By Using Picard Method, Ali Ebadian, Foroozan Farahrooz, Amirahmad Khajehnasiri
Applications and Applied Mathematics: An International Journal (AAM)
In this paper we prove convergence of the method of successive approximations used to approximate the solution of nonlinear two-dimensional Volterra-Fredholm integral equations and define the notion of numerical stability of the algorithm with respect to the choice of the first iteration. Also we present an iterative procedure to solve such equations. Finally, the method is illustrated by solving some examples.
Complex Solutions Of The Time Fractional Gross-Pitaevskii (Gp) Equation With External Potential By Using A Reliable Method, Nasir Taghizadeh, Mona N. Foumani
Complex Solutions Of The Time Fractional Gross-Pitaevskii (Gp) Equation With External Potential By Using A Reliable Method, Nasir Taghizadeh, Mona N. Foumani
Applications and Applied Mathematics: An International Journal (AAM)
In this article, modified (G'/G )-expansion method is presented to establish the exact complex solutions of the time fractional Gross-Pitaevskii (GP) equation in the sense of the conformable fractional derivative. This method is an effective method in finding exact traveling wave solutions of nonlinear evolution equations (NLEEs) in mathematical physics. The present approach has the potential to be applied to other nonlinear fractional differential equations. Based on two transformations, fractional GP equation can be converted into nonlinear ordinary differential equation of integer orders. In the end, we will discuss the solutions of the fractional GP equation with external potentials.
A New Approach For Solving System Of Local Fractional Partial Differential Equations, Hossein Jafari, Hassan K. Jassim
A New Approach For Solving System Of Local Fractional Partial Differential Equations, Hossein Jafari, Hassan K. Jassim
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we apply a new method for solving system of partial differential equations within local fractional derivative operators. The approximate analytical solutions are obtained by using the local fractional Laplace variational iteration method, which is the coupling method of local fractional variational iteration method and Laplace transform. Illustrative examples are included to demonstrate the high accuracy and fast convergence of this new algorithm. The obtained results show that the introduced approach is a promising tool for solving system of linear and nonlinear local fractional differential equations. Furthermore, we show that local fractional Laplace variational iteration method is able …