Solving Higher Order Nonlinear Differential Equation with Nonlocal Boundary Value Problem

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.

Positive Solutions to Nonlinear Higher-Order Nonlocal Boundary Value Problems for Fractional Differential Equations

and Applied Analysis 3 2. Background Materials and Lemmas For the convenience of the readers, in this section, we provide definitions of RiemannLiouville fractional integral and fractional derivative and some of their basic properties which will be helpful in the forth coming investigations. Definition 2.1 see 2, 5 . For a function φ : a,∞ → R, the Riemann-Liouville fractional integral of order...

Existence of Solutions for Nonlocal Boundary Value Problems of Higher-Order Nonlinear Fractional Differential Equations

and Applied Analysis 3 involving fractional differential equations the same applies to the boundary value problems of fractional differential equations . Moreover, the Caputo derivative for a constant is zero while the Riemann-Liouville fractional derivative of a constant is nonzero. For more details, see 17 . Lemma 2.4 see 28 . For q > 0, the general solution of the fractional differential equ...

Nonlocal Boundary Value Problem for Strongly Singular Higher-Order Linear Functional-Differential Equations

For strongly singular higher-order differential equations with deviating arguments, under nonlocal boundary conditions, Agarwal-Kiguradze type theorems are established, which guarantee the presence of the Fredholm property for the problems considered. We also provide easily verifiable conditions that guarantee the existence of a unique solution of the problem. 2000 Mathematics Subject Classific...

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