[PDF] Top 20 Positive solutions of fractional differential equation nonlocal boundary value problems

... [, +∞) → [, +∞) and g : [, ] × [, +∞) → [, +∞) are continuous,   x(s)dA(s) de- notes the Riemann-Stieltjes integral of x with respect to A, A : [, ] → R is a function of bounded variation and dA can be a signed ... See full document

... order differential and integral operators play an important role in the mathematical modeling of several real world ...and boundary value problems of fractional differential ... See full document

... of positive solutions for a periodic boundary value problem of a fractional differential equation in an ordered Banach space ...of solutions for the associated linear ... See full document

... The organization of this paper is as follows. In Sect. 2, we present some necessary def- initions from fractional calculus theory. In Sect. 3, we prove the main results about the existence of positive ... See full document

... The boundary value problem of fractional equations has emerged as a new branch in the fields of differential equations for their deep ...of fractional calculus frequently appears in various ... See full document

... For the convenience of the reader, we recall in this section some basic definitions on frac- tional calculus (see [, , ]) and we give some properties of the Green’s function G(x, t). Definition . The ... See full document

... the boundary value prob- lem (BVP for short in the sequel) ...of solutions for BVP ...of positive solution for BVP ...fourth-order boundary value ... See full document

... higher-dimension fractional equation systems are seldom ...the solutions to be positive. Since only positive solutions are useful for many applications, we investigate the ... See full document

... where D β 0+ , D α 0+ and D γ 0+ are the standard Riemann-Liouville derivatives with 1 <a ≤ 2, 0 <b ≤ 1, 0 <g ≤ 1, 0 ≤ a - g - 1, the constant s is a positive number and p - Laplacian operator is defined ... See full document

... of solutions for differential equations has been widely stud- ied by many scholars in the mathematical sense (see [–] and the references ...of positive solutions for the following periodic ... See full document

... one positive so- lution. By a positive solution of problem (S)-(BC) we mean a pair of functions (u, v) ∈ C([, ]) × C([, ]) satisfying (S) and (BC) with u(t) ≥ , v(t) ≥  for all t ∈ [, ] and u(t) ... See full document

... The rest of the paper is organized as follows. In Section 2, we give some preliminaries and a lemma which establishes a completely continuous operator. In Section 3, Theorems 3.1 and 3.2, and results for the existence of ... See full document

... However, third-order or higher-order derivatives do not have the convexity; to the best of our knowledge, no results are available for the existence of positive solutions for third- order or higher- order ... See full document

... Local in time existence of positive classical solutions of (1.1) can be obtained by using fixed point theorem [21], the representation formula and the contraction map- ping principle as in [13]. By the ... See full document

... This paper is organized as follows. In Section , we review some preliminaries and lem- mas. In Section , a theorem and five corollaries about the existence of at least one positive solution of problem ()-() are ... See full document

... nontrivial solutions for the higher nonlocal fractional differential equations ...the boundary conditions all involve fractional derivatives of unknown ... See full document

... Let the real Banach space E with the norm · be partially ordered by a cone P of E, i.e., u ≤ v if and only if v – u ∈ P, and P is said to be normal if there exists a positive constant N such that θ ≤ u ≤ v implies ... See full document

... of positive solutions for a fractional differential equation subject to BC ...a fractional differential equation with infinite-point boundary value conditions ...of ... See full document

... of fractional differential equations boundary value problems with p- Laplacian operator have also received much attention and have developed very rapidly, see ...following fractional ... See full document

... to fractional-order equations and inclusions in Banach spaces, let us mention [3, 5, 15–17, 20, 21, 23, 24, 27, 33, 34, 36], where vari- ous existence results were ...semilinear fractional differential ... See full document