Initial Value Problems with Generalized Fractional Derivatives and Their Solutions via Generalized Laplace Decomposition Method

Laplace Decomposition Method for Solving Singular Initial Value Problems

In this paper, Laplace Decomposition Method (LDM) which is coupling of Laplace Transform (LT) and Adomian’s Decomposition Method (ADM) is employed to construct the exact solution of two mathematical problems which arises in diverse fields of physics. It has been observed that this proposed coupling is very efficient and reliable for the solution of the nonlinear problems. Numerical results and ...

Solutions of initial and boundary value problems via F-contraction mappings in metric-like space

We present sufficient conditions for the existence of solutions of second-order two-point boundary value and fractional order functional differential equation problems in a space where self distance is not necessarily zero. For this, first we introduce a Ciric type generalized F-contraction and F- Suzuki contraction in a metric-like space and give relevance to fixed point results. To illustrate...

Numerical solutions of telegraph and laplace equations on cantor sets using local fractional laplace decomposition method

In this paper, the local fractional Laplace decomposition method is implemented to obtain approximate analytical solution of the telegraph and Laplace equations on Cantor sets. This method is a combination of the Yang-Laplace transform and the Adomian decomposition method. Some examples are given to illustrate the efficiency and accuracy of the proposed method to obtain analytical solutions to ...

An Algorithm for Solving Initial Value Problems Using Laplace Adomian Decomposition Method

The Adomian Decomposition Method (ADM) has been applied to a wide class of problems in physics, biology and chemical reactions. The method provides the solution in a rapid convergent series with computable terms. This method was successfully applied to nonlinear differential delay equations [1], a nonlinear dynamic systems [2], the heat equation [3,4], the wave equation [5], coupled nonlinear p...

Numerical solution of fuzzy initial value problems under generalized dierentiability by HPM