SOLVABILITY FOR A NONLINEAR FRACTIONAL DIFFERENTIAL EQUATION

Existence of positive solutions for a boundary value problem of a nonlinear fractional differential equation

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.

Numerical approach for solving a class of nonlinear fractional differential equation

‎It is commonly accepted that fractional differential equations play‎ ‎an important role in the explanation of many physical phenomena‎. ‎For‎ ‎this reason we need a reliable and efficient technique for the‎ ‎solution of fractional differential equations‎. ‎This paper deals with‎ ‎the numerical solution of a class of fractional differential‎ ‎equation‎. ‎The fractional derivatives are described...

Solvability of Periodic Boundary-value Problems for Second-order Nonlinear Differential Equation Involving Fractional Derivatives

This article concerns the existence of solutions to periodic boundaryvalue problems for second-order nonlinear differential equation involving fractional derivatives. Under certain linear growth condition of the nonlinearity, we obtain solutions, by using coincidence degree theory. An example illustrates our results.

Triple Positive Solutions for Boundary Value Problem of a Nonlinear Fractional Differential Equation

Fractional Runge-kutta Methods for Nonlinear Fractional Differential Equation

Based on high order approximation of L-stable RungeKutta methods for the Riemann-Liouville fractional derivatives, several classes of high order fractional Runge-Kutta methods for solving nonlinear fractional differential equation are constructed. Consistency, convergence and stability analysis of the numerical methods are given. Numerical experiments show that the proposed methods are efficien...