Solving Cauchy reaction-diffusion equation by using Picard method

Abstract

In this paper, Picard method is proposed to solve the Cauchy reaction-diffusion equation with fuzzy initial condition under generalized H-differentiability. The existence and uniqueness of the solution and convergence of the proposed method are proved in details. Some examples are investigated to verify convergence results and to illustrate the efficiently of the method. Also, we obtain the switching points in examples.

Computation of solution to fractional order partial reaction diffusion equations

“…The numerical simulation to space fractional diffusion equations have been performed in [10] , [11] . The exact solutions of nonlinear biological population models of fractional order has been obtained in [12] by optimal homotopy method (OHAM). On using OHAM, the solution of Burgers- Huxley models [13] has been computed.…”

A Modified Techniques of Fractional-Order Cauchy-Reaction Diffusion Equation via Shehu Transform

“…The model defined by equations ( 2) and ( 3) is called the characteristic Cauchy model in the domain Ω = R × R + , and the model given by equations ( 2) and ( 4) is called the noncharacteristic Cauchy equation in the domain Ω = R + × R, using different analytical and numerical methods to solve reaction diffusion equation, such as Picard technique [10], homotopy perturbation technique [3], differential transformation technique and variation iteration technique [11], Adomian decomposition method [12], homotopy analysis method [13], fractional iteration algorithm I [14], new Sumudu transform iterative method [15], and finitedifference discretization scheme [16].…”

A fractional system of Cauchy‐reaction diffusion equations by adopting Robotnov function

“…In this work, the author has proposed an iterative method without any linearization or discrimination. Picard's method is utilized in [10]. Recently, Kumar et al introduced a modified analytical technique for solving CRDE using the HAM [28].…”