A new iterative method introduced by Daftardar‐Gejji and Jafari (2006) (DJ Method) is an efficient technique to solve nonlinear functional equations. In the present paper, sufficiency conditions for convergence of DJM have been presented. Further equivalence Adomian decomposition established.

Abstract In this article, we apply the new iterative method proposed by Daftardar‐Gejji and Jafari (J Math Anal Appl 316, (2006), 753–763) for solving various linear nonlinear evolution equations. The results obtained are compared with existing methods. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010

The fundamental description of relaxation (T 1 and T 2 ) in nuclear magnetic resonance (NMR) is provided by the Bloch equation, an integer-order ordinary differential equation that interrelates precession magnetization with time- space-dependent relaxation. In this paper, we propose a fractional order includes extended model time delays. derivative embeds fading power law form system memory while delay averages present value earlier one. analysis shows different patterns stability behavior...

Partialintegro-differential equations (PIDE) occur naturally in various fields of science, engineering and social sciences. In this article, we propose a most general form linear PIDE with convolution kernel. We convert the proposed to an ordinary differential equation (ODE) using Laplace transform (LT). Solving ODE applying inverse LT exact solution problem is obtained. It observed that simple reliable technique for solving such equations. A variety numerical examples are presented show...

A fractional version of logistic equation is solved using new iterative method proposed by Daftardar-Gejji and Jafari (2006). Convergence the series solutions obtained discussed. The are compared with Adomian decomposition homotopy perturbation method.

This paper deals with the stability and bifurcation analysis of a general form equation Dαx(t)=g(x(t),x(t−τ)) involving derivative order α ∈ (0, 1] constant delay τ ≥ 0. The equilibrium points is presented in terms regions critical surfaces. We provide necessary condition to exist chaos system also. A wide range differential equations can be analyzed using results proposed this paper. illustrative examples are provided explain theory.

The differential equations involving two discrete delays are helpful in modeling different processes one model. We provide the stability and bifurcation analysis fractional order delay equation Dαx(t)=ax(t)+bx(t−τ)−bx(t−2τ) ab-plane. Various regions of include stable, unstable, single stable region (SSR), switch (SS). In region, system is for all values. SSR has a critical value that bifurcates unstable behavior. Switching behaviors observed SS region.

Fractional order differential and difference equations are used to model systems with memory. Variable fractional proposed where the memory changes in time. We investigate stability conditions for linear variable is periodic function period $T$. give a general procedure arbitrary $T$ $T=2$ $T=3$, we exact results. For $T=2$, find that lower determines of equations. odd $T$, numerical simulations indicate can approximately determine from mean value variables.