On existence and uniqueness of fractional integrodifferential equations with an integral fractional boundary condition

Existence Results for Nonlinear Boundary Value Problems of Fractional Integrodifferential Equations with Integral Boundary Conditions

Existence and Uniqueness Theorem for Fractional Differential Equation with Integral Boundary Condition

We have investigated the existence and uniqueness solutions of the nonlinear fractional differential equation of an arbitrary order with integral boundary condition. The result is an application of the Schauder fixed point theorem and the Banach contraction principle.

Existence and Uniqueness of Solution for Fractional Differential Equations with Integral Boundary Conditions

     Dx(t) + f(t, x(t), x(t)) = 0, t ∈ (0, 1), x(0) = ∫ 1 0 g0(s, x(s))ds, x(1) = ∫ 1 0 g1(s, x(s))ds, x(0) = 0, k = 2, 3, · · · , [α]− 1. By means of the Banach contraction mapping principle, some new results on the existence and uniqueness are obtained. It is interesting to note that the sufficient conditions for the existence and uniqueness of solutions are dependent on the order α.

Existence and Uniqueness of Fractional Differential Equations with Integral Boundary Conditions

In this article, the recently developed monotonous iterative method is used to investigate fractional differential equations involving Riemann-Liouville differential operators with integral boundary conditions. The existence and uniqueness of solutions are obtained.

Existence and Uniqueness of Solutions for Nonlinear Fractional Differential Equations with Integral Boundary Conditions

In this paper, we study existence and uniqueness of solutions to nonlinear fractional differential equations with integral boundary conditions in an ordered Banach space. We use the Caputo fractional differential operator and the nonlinearity depends on the fractional derivative of an unknown function. For the existence of solutions, we employ the nonlinear alternative of Leray-Schauder and the...