*Correspondence: [email protected] Department of Mathematics, Northwest Normal University, Lanzhou, 730070, People’s Republic of China Abstract This paper deals with the existence and uniqueness of mild solutions for a class of fractional evolution equations with nonlocal initial conditions. We present some local growth conditions on a nonlinear part and a nonlocal term to guarantee the existen...

This paper studies a nonlinear fractional differential equation of an arbitrary order with four-point nonlocal integral boundary conditions. Some existence results are obtained by applying standard fixed point theorems and Leray-Schauder degree theory. The involvement of nonlocal parameters in four-point integral boundary conditions of the problem makes the present work distinguished from the a...

In this paper we discuss about nonlinear pseudoparabolic equations with nonlocal boundary conditions and their results. An effective error estimation for this method altough has not yet been discussed. The aim of this paper is to fill this gap.

An elliptic equation of order 2m with general nonlocal boundary-value conditions, in a plane bounded domain G with piecewise smooth boundary, is considered. Generalized solutions belonging to the Sobolev space Wm 2 (G) are studied. The Fredholm property of the unbounded operator corresponding to the elliptic equation, acting on L2(G), and defined for functions from the space Wm 2 (G) that satis...