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In this paper, we consider integral boundary value problems of nonlinear fractional differential equations. Existence results of positive solutions for the problem are obtained based on the Guo-Krasnoselskii theorem and the Five functional fixed point theorem. Simple examples follow the main results in successive sections. [ABSTRACT FROM AUTHOR]

Let T ⊆ R be a time scale. The purpose of this paper is to present sufficient conditions for the existence of multiple positive solutions of the following Lidstone boundary value problem on time scales: (− 1) n y Δ (2 n) (t) = f (t , y (t)) , t ∈ [ a , b ] T , y Δ (2 i) (a) = y Δ (2 i) (σ 2 n − 2 i (b)) = 0 , i = 0 , 1 , ... , n − 1. Existence of multiple positive solutions is established using fixed point methods. At the end some examples are also given to illustrate our results. [ABSTRACT FROM AUTHOR]

In this work, two different boundary value problems of fractional q-difference equation are discussed. The first one is fractional q-difference equation with integral boundary conditions and the other one is three point boundary value problem of fractional q-difference equation with p-Laplacian. By using fixed point theorems, some sufficient conditions that guarantee the existence and uniqueness of solutions are given. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the existence of symmetric positive solutions for the systems of higherorder boundary value problems on time scales. Our results extend some recent work in the literature. The analysis of this paper mainly relies on the monotone iterative technique. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with proving the existence of solutions for four point fractional differential equations with p-Laplacian operator. We obtain the existence of at least one solution for the problem applying Schauder fixed-point theorem. [ABSTRACT FROM AUTHOR]

This work is concerned with the existence of positive solutions to a nonlinear nonlocal first-order multipoint problem. Here the nonlinearity is allowed to take on negative values, not only positive values. [ABSTRACT FROM AUTHOR]

This paper presents an efficient method for the computation of two highly oscillatory integrals having logarithmic and Cauchy-logarithmic singularities. This approach first requires the transformation of the original oscillatory integrals into a sum of line integrals with semi-infinite intervals. Afterwards, the coefficients of the three-term recurrence relation that satisfy the orthog- onal polynomial are obtained by using the method based on moments, where classical Laguerre and Gautschi's logarithmic weight functions are employed. The algorithm reveals that with fixed n, the method is capable of achieving significant figures within a short time. Furthermore, the approach yields higher accuracy as the frequency increases. The results of numerical experiments are given to substantiate our theoretical analysis. [ABSTRACT FROM AUTHOR]