[PDF] Top 20 Iterative technique for coupled integral boundary value problem of non integer order differential equations

... differential equations of fractional order. In last few decades, boundary value problems of differential equations of fractional order were greatly studied by many researchers for ... See full document

... monotone iterative technique combined with the method of upper and lower so- lutions is a powerful tool for proving the existence of solutions of differential equa- tions/system (see [–] and the references ... 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 ... See full document

... first order boundary value problems for fractional differential equations and inclusions with fractional integral boundary ...fractional differential ... See full document

... The rest of this paper is organized as follows. In Section 2, we establish a new comparison principle and discuss the existence and uniqueness of the solution for first order impulsive functional differential ... See full document

... multi-point boundary value problems for ordinary differential equations have been well studied, especially on a compact ...three-point boundary value problems for nonlinear ... See full document

... differential equations have recently been addressed by several researchers for a variety of ...differential equations arise in many engineering and sci- entific disciplines as the mathematical modeling of ... See full document

... In this paper, we investigate a class of nonlinear two-term fractional differential equations involving two fractional orders δ ∈ (1, 2] and τ ∈ (0, δ ) with integral boundary value conditions. ... See full document

... two-point boundary value conditions, by using the monotone iterative technique, combined with the method of upper and lower solutions; for details, see ...fractional integral bound- ary ... See full document

... singular coupled integral boundary value problem of nonlinear higher-order fractional q-difference ...the problem are ... See full document

... Since in many situations, such as nonlinear analysis and optimization, finding the exact solution of differential equations is almost difficult or impossible, we consider approxi- mate solutions. It is important to ... See full document

... the boundary value problems for impulsive fractional differential equations (see [1, 15–26, 30, ...differential coupled systems is more compli- cated and challenged than the study on a single ... See full document

... We treat the existence of monotonic iteration positive solutions to a third-order boundary value problem with advanced arguments and Stieltjes integral boundary conditions. In ... See full document

... of boundary value problems of nonlinear fractional differential equations whose nonlinear term depends on a lower-order fractional derivative with fractional separated boundary ... See full document

... a boundary value problem for a class of third-order operator-differential equations with a real and real multiple ...differential equations whose characteristic equations ... See full document

... be non-negative continuous convex functionals on K, α be a non-negative continuous concave functional on K, and φ be a non-negative continuous functional on K satisfying φ(λu) ≤ λφ(u) for 0 ≤ λ ≤ 1, ... See full document

... We should mention that 1.1, 1.2 are more general than equations considered in 13, 18 since f, J both contain x and its derivative. So our result is still new even when 1.1, 1.2 reduce to equations studied ... See full document

... if non-negative numbers T – , T + satisfy () (or ()), then equality holds in condition () (or ()) for a unique solution x of problem ()-() for some linear positive operators T – , T + with norms T ... See full document

... Proof of Theorem 3.4. From the conditions (3.11) and (3.13) it follows that the conditions (3.2) and (3.7) are satisfied with c = | h(0) | and q ≡ | Q(0) | . Consequently, the assump- tions of Theorem 3.2 are fulfilled. ... See full document

... two point boundary value problem associated with coupled second order equations to which a fourth order linear differential equation is reduced... An attractive feature.[r] ... See full document