The fractional order Susceptible-Infected-Recovered (SIR) epidemic model of childhood disease is considered. Laplace–Adomian Decomposition Method is used to compute an approximate solution of the system of nonlinear fractional differential equations. We obtain the solutions of fractional differential equations in the form of infinite series. The series solution of the proposed model converges rapidly to its exact value. The obtained results are compared with the classical case.

The importance of the model reduction techniques cannot be denied or ignored for a number of combustion problems in chemical sciences. We examine an analysis of very well-known method by Mass and Pope by measuring the influence of physical processes on the water-gas shift reaction (WGSR). We observe that if the process of physical and chemical reactions is coupled, this will lead to a very dramatic effect. An adaptive parameterization technique is developed for the numerical implementation. Through proper algorithm and grid size variations, the approximate solution is obtained and further refined with the method of invariant grids. Consequently, it leads us to a vicious effect on CPU when we extended this idea to higher dimensions

This paper considers the approximation of solution for a fractional order biological population model. The fractional derivative is considered in the Caputo sense. By using Laplace Adomian decomposition method (LADM), we construct a base function and provide deformation equation of higher order in a simple equation. The considered scheme gives us a solution in the form of rapidly convergent infinite series. Some examples are used to show the efficiency of the method. The results show that LADM is efficient and accurate for solving such types of nonlinear problems.

In the present manuscript we incorporate fractional order Caputo derivative to study a class of non-integer order differential equation. For existence and uniqueness of solution some results from fixed point theory is on our disposal. The method used for exploring these existence results is topological degree method and some auxiliary conditions are developed for stability analysis. For further elaboration an illustrative example is provided in the last part of the research article.

In this paper, we apply new type monotone iterative technique which is very rarely used to find iterative solutions for boundary value problem (BVPs) of nonlinear fractional order differential equations (NFODEs). With the help of the aforesaid technique, we establish two sequences of upper and lower solutions for the considered BVP. Further the procedure is testified by providing suitable examples.