in this paper, using the fixed point theory in cone metric spaces, we prove the existence of a unique solution to a first-order ordinary differential equation with periodic boundary conditions in banach spaces admitting the existence of a lower solution.

this paper studies a fractional boundary value problem of nonlineardifferential equations of arbitrary orders. new existence and uniquenessresults are established using banach contraction principle. other existenceresults are obtained using schaefer and krasnoselskii fixed point theorems.in order to clarify our results, some illustrative examples are alsopresented.

In this paper, we concerned with positive solutions for higher order m-point nonlinear fractional boundary value problems with integral boundary conditions. We establish the criteria for the existence of at least one, two and three positive solutions for higher order m-point nonlinear fractional boundary value problems with integral boundary conditions by using a result from the theory of fixed...

a class of new methods based on a septic non-polynomial spline function for the numerical solution one-dimensional bratu's problem are presented. the local truncation errors and the methods of order 2th, 4th, 6th, 8th, 10th, and 12th, are obtained. the inverse of some band matrixes are obtained which are required in proving the convergence analysis of the presented method. associated bound...

this paper is devoted to the study of establishing sufficient conditions forexistence and uniqueness of positive solution to a class ofnon-linear problems of fractional differential equations. the boundary conditionsinvolved riemann-liouville fractional order derivative and integral. further, the non-linear function $f$ containfractional order derivative which produce extra complexity. thank to...

in this paper, we prove the existence of the solution for boundary value prob-lem(bvp) of fractional dierential equations of order q 2 (2; 3]. the kras-noselskii's xed point theorem is applied to establish the results. in addition,we give an detailed example to demonstrate the main result.

in this paper, we study a coupled system of nonlinear fractional differential equations with multi-point boundary condi- tions. the differential operator is taken in the riemann-liouville sense. applying the schauder fixed-point theorem and the contrac- tion mapping principle, two existence results are obtained for the following system d^{alpha}_{0+}x(t)=fleft(t,y(t),d^{p}_{0+}y(t)right), t in (0,...

In this paper, we study the existence of three solutions to the following nonlinear m-point boundary value problem  u′′(t) + βu(t) = h(t)f(t, u(t)), 0 < t < 1, u′(0) = 0, u(1) = m−2 ∑ i=1 αiu(ηi), where 0 < β < π2 , f ∈ C([0, 1] × R ,R). h(t) is allowed to be singular at t = 0 and t = 1. The arguments are based only upon the Leggett-Williams fixed point theorem. We also prove nonexist results.