[PDF] Top 20 Positive solutions for discrete fractional initial value problem

... of fractional calculus and fractional differential ...for fractional differential ...boundary value problems for fractional differential ... See full document

... of solutions to boundary value problems associated with fractional differential equations have recently been attracted the attention of many researchers, see for example [1, 3, 4, 5, 8, 12, 13, 16, ... See full document

... boundary value problems for fractional differential equations have been extensively studied, most of the studies focus on scalar equations and the fractional order between 1 and ...for ... See full document

... In this paper, we prove the existence of positive solutions to the boundary value prob- lem (1.1)–(1.2) by the Schauder fixed point theorem and the method of upper and lower solutions. Then, we ... See full document

... a positive eigenvector. Moreover, if A + (θ ) has no positive eigenvectors corresponding to an eigenvalue greater than one, then there exists r  >  such ... See full document

... consequently, letting n → ∞ in (3.2), we see that u ∗ = P ◦ F(u ∗ ). By the definition of P, it is easy to see that u ∗ is the corresponding solution of the linear periodic boundary value problem (2.2), when ... 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

... In [, ], Sun and Zhang discussed a class of singular superlinear and sublinear Sturm- Liouville problems, respectively. In the two papers, the Sturm-Liouville problems are considered under some conditions concerning ... See full document

... of solutions for initial value problem for a class of nonlinear Caputo-Hadamard fractional differential equations with nonlocal ... See full document

... bounded solutions for a class of initial value problem on the half-line for fractional differential equations involving Caputo fractional derivative with a nonlinear term ... See full document

... Proof By using a similar method to the proof of Theorem ., we can prove that for IVP (.) and IVP (.) there exist unique mild solutions u and u ˜ on [, a] for an appropri- ate constant a > , ... See full document

... on discrete problem via critical point theory, the authors are interested in the existence of at least one solution or infinitely many ...that problem (.) has many solutions if the ... See full document

... The rest of this paper has the following structure. In Section , we recall some basic definitions of fractional calculus, establish some lemmas and use symbols to replace with some formula which plays a pivotal ... See full document

... of positive solutions for boundary value problem ...of positive solu- tions are ...discuss fractional p-Laplacian with lower and upper solution ...Riesz fractional ... See full document

... boundary value problems, initiated by Il’in and Moi- seev [], has been addressed by many ...boundary value problem (see []); many problems in the theory of elastic stability can be ... See full document

... one positive solution of problem P by using Guo-Krasnoselskii fixed point theorem on cone; then, under some sufficient conditions on the nonlinear source term, we apply Avery-Peterson theorem to prove the ... See full document

... We established the existence of positive solutions for the singular fractional differential equation infinite-point BVP (1.1) using the fixed point index theory in cones. Note that the nonlinearity may ... See full document

... In this paper, we prove existence of positive solutions to a nonlinear fractional boundary value problem involving a p-Laplacian operator. Then, under some mild assumptions on the ... See full document

... Lemma 2.5 [9] Suppose that A : C[0, 1] → C[0, 1] is a completely continuous linear operator and A(P ) ⊂ P. If there exist ψ ∈ C[0, 1]\(−P) and a constant c > 0 such that cAψ ≥ ψ, then the spectral radius r(A) 6= 0 and ... See full document

... The rest of the paper is organized as follows. In Section , we introduce some lemmas and definitions which will be used later. In Section , the existence of positive solutions for the boundary value ... See full document