[PDF] Top 20 Solutions for a fractional difference boundary value problem

... 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 nonlinearity is ... See full document

... to boundary value problems at res- onance for ordinary or fractional differential ...positive solutions by using a fixed point theorem of increasing ... See full document

... where 2 < α ≤ 3, 0 < β ≤ 1, the nonlinearity f (t, u) may change sign on some set. By means of the monotone iterative technique, the existence of nontrivial solutions or positive so- lutions is obtained. ... See full document

... The arguments for BVP (1.2) are based on a monotone iterative technique. It is impor- tant that the Green’s function associated with BVP (1.2) is nonnegative, which is different from that of BVP (1.1). In this part, not ... See full document

... 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 existence of at least three ... See full document

... where  < α, β ≤ , and k : [a, b] → R is a continuous function. We write (.) as an equiv- alent integral equation and then, by using some properties of its Green function and the Guo-Krasnoselskii fixed point ... See full document

... that fractional difference equations have been extensively studied in recent ...discrete fractional boundary value problems are also ...positive solutions for coupled systems of ... See full document

... Morse theory has been proved very useful in proving the existence and multiplicity of solutions of operator equations with variational frameworks. However, it is well known that the minimax methods is also a ... See full document

... Proof By using Lemmas . and ., we can see that there exists u ∈ N such that I(u) = m = inf N I. Then u is a critical point of I| N . From Lemma . we have I (u) = . So boundary value problem ... See full document

... the fractional difference by choice is a normal method of letting the index of differences, in the criterion appearance for the nth difference, to be any number (real or ...the fractional difference operator ... See full document

... of fractional calculus and its widespread applications in sev- eral disciplines clearly indicate the interest of researchers and modelers in the ...of fractional calculus have been effectively used in ... See full document

... towards fractional differential equations as many phenomena in various branches of science and engineering are ...of fractional differential equations due to Lakshmikantham ...Periodic boundary ... See full document

... We emphasize that the results obtained for problem (1.1) are new and significantly con- tribute to the existing literature on p-Laplacian problems with fractional conformable derivatives. In order to ... See full document

... of fractional differential equations and their applications has received inten- sive ...on fractional difference equations have appeared ...discrete fractional calculus. In [], Atici and Eloe studied ... See full document

... the fractional q-difference using a single- derivative (Riemann–Liouville or Caputo derivative), in this paper, we consider the exis- tence and uniqueness of the solution to the fractional q-difference ... See full document

... of fractional dif- ferential equations and fractional difference equations has been ...of fractional partial differential equations that involve the Riemann-Liouville fractional partial ... See full document

... Fractional differential equations have been of great interest recently because of their intensive applications in economics, financial mathematics and other applied science (see [1]-[13] and the references ... See full document

... The plan of this paper is as follows. We first give the form of solutions of problem (.), second we prove the existence and uniqueness of a solution to problem (.) by the con- traction mapping ... 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

... where fractional boundary value problems have been studied by different methods such as the upper and lower solutions method, fixed point theorems, successive approximations method, Mawhin ... See full document