In this article, we introduce the local fractional integral iterative method and the local fractional new iterative method for solving the local fractional differential equations. Also, we perform a comparison between the results obtained by these 2 local fractional methods with the results obtained by some other local fractional methods. The obtained results illustrate the significant features of the 2 methods that are both very effective and straightforward for solving the differential equations with local fractional derivative compared with the other local fractional methods.
An unsteady axisymmetric flow of nonconducting, Newtonian fluid squeezed between two circular plates is proposed with slip and no-slip boundaries. Using similarity transformation, the system of nonlinear partial differential equations of motion is reduced to a single fourth-order nonlinear ordinary differential equation. By using the basic definitions of fractional calculus, we introduced the fractional order form of the fourth-order nonlinear ordinary differential equation. The resulting boundary value fractional problems are solved by the new iterative and Picard methods. Convergence of the considered methods is confirmed by obtaining absolute residual errors for approximate solutions for various Reynolds number. The comparisons of the solutions for various Reynolds number and various values of the fractional order confirm that the two methods are identical and therefore are suitable for solving this kind of problems. Finally, the effects of various Reynolds number on the solution are also studied graphically.
In this article, we propose the new iterative method and introduce the integral iterative method to solve linear and nonlinear Fokker-Planck equations and some similar equations. The results obtained by the two methods are compared with those obtained by both Adomian decomposition and variational iteration methods. Comparison shows that the two methods are more effective and convenient to use and overcome the difficulties arising in calculating Adomian polynomials and Lagrange multipliers, which means that the considered methods can simply and successfully be applied to a large class of problems.
Abstract. In this work, we are concerned with the Cauchy problem of a delay stochastic differential equation of arbitrary (fractional) orders. The existence (local) of a unique mean square continuous solution is proved. The continuous dependence of the solution on the initial random variable is studied.Mathematics subject classification (2010): 26A33, 34K50.
In this work, some analytical techniques viz. homotopy perturbation method, new iterative method and integral iterative method are used to solve nonlinear fractional differential equations such as the equation governing the unsteady flow of a polytropic gas with time-fractional derivative. Comparisons are made between the considered techniques and also between their results. The obtained results reveal that these techniques are very simple and effective and give the solution in series form which in closed form gives the exact solution also, reveal that the integral iterative technique is simpler and shorter in its computational procedures and time than the other techniques.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.