448 research outputs found
Numerical Solutions for the Time and Space Fractional Nonlinear Partial Differential Equations
We implement relatively analytical techniques, the homotopy perturbation method, and variational iteration method to find the approximate solutions for time and space fractional Benjamin-Bona Mahony equation. The fractional derivatives are described in the Caputo sense. These methods are used in applied mathematics to obtain the analytic approximate solutions for the nonlinear Bejamin-Bona Mahoney (BBM) partial fractional differential equation. We compare between the approximate solutions obtained by these methods. Also, we present the figures to compare between the approximate solutions. Also, we use the fractional complex transformation to convert nonlinear partial fractional differential equations to nonlinear ordinary differential equations. We use the improved -expansion function method to find exact solutions of nonlinear fractional BBM equation
A new modified homotopy perturbation method for fractional partial differential equations with proportional delay
In this paper, we suggest and analyze a technique by combining the Shehu transform method and the homotopy perturbation method. This method is called the Shehu transform homotopy method (STHM). This method is used to solve the time-fractional partial differential equations (TFPDEs) with proportional delay. The fractional derivative is described in Caputo's sense. The solutions proposed in the series converge rapidly to the exact solution. Some examples are solved to show the STHM is easy to apply
A new approach for solving nonlinear Thomas-Fermi equation based on fractional order of rational Bessel functions
In this paper, the fractional order of rational Bessel functions collocation
method (FRBC) to solve Thomas-Fermi equation which is defined in the
semi-infinite domain and has singularity at and its boundary condition
occurs at infinity, have been introduced. We solve the problem on semi-infinite
domain without any domain truncation or transformation of the domain of the
problem to a finite domain. This approach at first, obtains a sequence of
linear differential equations by using the quasilinearization method (QLM),
then at each iteration solves it by FRBC method. To illustrate the reliability
of this work, we compare the numerical results of the present method with some
well-known results in other to show that the new method is accurate, efficient
and applicable
Homotopy perturbation method to space–time fractional solidification in a finite slab
AbstractA mathematical model describing the space and time fractional solidification of fluid initially at its freezing temperature contained in a finite slab under the constant wall temperature is presented. The approximate analytical solution of this problem is obtained by the homotopy perturbation method. The results thus obtained are compared with exact solution of integer order (β=1,α=2) and are good agreement. The problem has been studied in detail by considering different order time and space fractional derivatives. The temperature distribution and the moving interface position for different fractional order space and time derivatives are shown graphically. The model and the solution are the generalization of the previous works and include them as special cases
Modified homotopy perturbation method coupled with Laplace transform for fractional heat transfer and porous media equations
The purpose of this paper is to extend the homotopy perturbation method to
fractional heat transfer and porous media equations with the help of the
Laplace transform. The fractional derivatives described in this paper are in
the Caputo sense. The algorithm is demonstrated to be direct and
straightforward, and can be used for many other non-linear fractional
differential equations
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