Abstract: In this article, an approximate analytical solution of coupled nonlinear equations with fractional time derivative are obtained with the help of approximate analytical method of nonlinear problem called the Homotopy Perturbation Method. By using initial condition, the explicit solutions of the coupled equation have been derived which demonstrate the potentiality, validity, effectivene...

In this study, Reduced Differential Transform Method (RDTM) is applied to some systems of nonlinear PDEs. The concept of RDTM is introduced birefly and RDTM is examined for system of nonlinear PDEs. The main advantage of the RDTM is the fact that it provides to its user an analytical approximation, in many cases an exact solution, in a rapidly convergent sequence with elegantly computed terms. ...

The goal of this paper is to examine the possible extension of the singular perturbation differential equation to the concept of fractional order derivative. To achieve this, we presented a review of the concept of fractional calculus. We make use of the Laplace transform operator to derive exact solution of singular perturbation fractional linear differential equations. We make use of the meth...

It is shown that, if the residual of a stable numerical solution is sufficiently small, there exists a nearby exact solution for which an a posteriori error estimate holds. This result demonstrates that it is not necessary to assume the existence of exact solutions in a posteriori error analysis for nonlinear equations. The concept is analyzed in an abstract Banach space setting and its practic...

Oscillations of a system with strong quadratic damping are considered. For the exact analytical form of the energy-displacement function the explicit form of the maximal amplitudes of vibration are obtained by introducing the Lambert W function. Comparing the neighbor maximal amplitudes and the corresponding energies the conclusions about the energy dissipation is given. The approximate solutio...

r. ewing, o. liev, r. lazarov and a. naumovich in [1] proposed a finite volume discretization for one dimensional biot poroelasticity system in multilayer domains. their discretization and exact solution are invalid. we derive valid discretization and exact solution. finally, our numerical solution is compared with known exact solution in discrete l2 norm.

The objective of this article is to carry out an approximate analytical solution of the time fractional order Cauchy-reaction diffusion equation by using a semi analytical method referred as the fractional-order reduced differential transform method (FRDTM). The fractional derivative is illustrated in the Caputo sense. The FRDTM is very efficient and effective powerful mathematical tool for sol...

A mathematical solution for solute transport in a three-dimensional porous medium with a patch source under steady-state, uniform ground water flow conditions was developed by Domenico (1987). The solution derivation strategy used an approximate approach to solve the boundary value problem, resulting in a nonexact solution. Variations of the Domenico (1987) solution are incorporated into the so...