this paper presents conditions for the existence and multiplicity of positive solutions for a boundary value problem of a nonlinear fractional differential equation. we show that it has at least one or two positive solutions. the main tool is krasnosel'skii fixed point theorem on cone and fixed point index theory.

In this paper, a new construction of exact solutions based on the improved generalized Riccati equation mapping method with modified Reimann-Luiviile fractional derivative and symbolic computation is proposed for seeking abundant solutions of the space-time fractional fifth-order nonlinear Sawada-Kotera equation. The proposed method is very simple, direct, effective and convenient for obtaining...

In this article, the modified simple equation method has been extended to celebrate the exact solutions of nonlinear partial time-space differential equations of fractional order. Firstly, the fractional complex transformation has been implemented to convert nonlinear partial fractional differential equations into nonlinear ordinary differential equations. Afterwards, modified simple equation m...

Dynamic systems in many branches of science and industry are often perturbed by various types of environmental noise. Analysis of this class of models are very popular among researchers. In this paper, we present a method for approximating solution of fractional-order stochastic delay differential equations driven by Brownian motion. The fractional derivatives are considered in the Caputo sense...

In this work, some new interval oscillation criteria for solutions of a class of nonlinear fractional differential equations are established by using a generalized Riccati function and inequality technique. For illustrating the validity of the established results, we also present some applications for them. Key–Words: Oscillation; Interval criteria; Qualitative properties; Fractional differenti...

Many of nonlinear systems in the field of engineering such as nano-resonator and atomic force microscope can be modeled based on Duffing equation. Analytical frequency response of this system helps us analyze different interesting nonlinear behaviors appearing in its response due to its rich dynamics. In this paper, the general form of Duffing equation with cubic nonlinearity as well as par...

In this article, we verify existence and uniqueness of positive and nondecreasing solution for nonlinear boundary value problem of fractional differential equation in the form $D_{0^{+}}^{alpha}x(t)+f(t,x(t))=0, 0

Direct Simulation Monte Carlo (DSMC) is a particle-based simulation method for gas dynamics. The method can be viewed as either a simplified molecular dynamics (DSMC being several orders of magnitude faster) or as a Monte Carlo method for solving the time-dependent nonlinear Boltzmann equation. The DSMC method has been used successfully in the study of rarefied gas flows for several decades but...

Numerical methods are used to find exact solution for the nonlinear differential equations. In the last decades Iterative methods have been used for solving fractional differential equations. In this paper, the Homotopy perturbation method has been successively applied for finding approximate analytical solutions of the fractional nonlinear Klein–Gordon equation can be used as numerical algorit...