Eigenvalue Problem of Nonlinear Semipositone Higher Order Fractional Differential Equations

Eigenvalue Problem of Nonlinear Semipositone Higher Order Fractional Differential Equations

and Applied Analysis 3 Lemma 2.1 see 8, 9 . 1 If x ∈ L1 0, 1 , ρ > σ > 0, and n ∈ N, then IIx t I x t , DtIx t Iρ−σx t , 2.4 DtIx t x t , d dtn Dtx t Dt x t . 2.5 2 If ν > 0, σ > 0, then Dttσ−1 Γ σ Γ σ − ν t σ−ν−1. 2.6 Lemma 2.2 see 8 . Assume that x ∈ L1 0, 1 and μ > 0. Then IDtx t x t c1tμ−1 c2tμ−2 · · · cntμ−n, 2.7 where ci ∈ R i 1, 2, . . . , n , n is the smallest integer greater than or eq...

Semipositone higher-order differential equations

Krasnoselskii’s fixed-point theorem in a cone is used to discuss the existence of positive solutions to semipositone conjugate and (n, p) problems. @ 2004 Elsevier Ltd. All rights reserved. Keywords-Existence, Positive solution, Semipositone, Conjugate and (n,p) problems.

Eigenvalue Problem for a Class of Nonlinear Fractional Differential Equations

In this paper, we study eigenvalue problem for a class of nonlinear fractional differential equations D 0+u(t) = λf(u(t)), 0 < t < 1, u(0) = u(1) = u′(0) = u′(1) = 0, where 3 < α ≤ 4 is a real number, D 0+ is the Riemann–Liouville fractional derivative, λ is a positive parameter and f : (0,+∞)→ (0,+∞) is continuous. By the properties of the Green function and Guo–Krasnosel’skii fixed point theo...

Multiple Positive Solutions for Nonlinear Semipositone Fractional Differential Equations

On boundary value problems of higher order abstract fractional integro-differential equations

The aim of this paper is to establish the existence of solutions of boundary value problems of nonlinear fractional integro-differential equations involving Caputo fractional derivative by using the techniques such as fractional calculus, H"{o}lder inequality, Krasnoselskii's fixed point theorem and nonlinear alternative of Leray-Schauder type. Examples are exhibited to illustrate the main resu...