On Boundary Value Problems for Parabolic Equations of Higher Order in Time

Boundary Value Problems for Higher Order Parabolic Equations

We consider a constant coefficient parabolic equation of order 2m and establish the existence of solutions to the initial-Dirichlet problem in cylindrical domains. The lateral data is taken from spaces of Whitney arrays which essentially require that the normal derivatives up to order m−1 lie in L2 with respect to surface measure. In addition, a regularity result for the solution is obtained if...

On boundary value problems of higher order abstract fractional integro-differential equations

The aim of this paper is to establish the existence of solutions of boundary value problems of nonlinear fractional integro-differential equations involving Caputo fractional derivative by using the techniques such as fractional calculus, H"{o}lder inequality, Krasnoselskii's fixed point theorem and nonlinear alternative of Leray-Schauder type. Examples are exhibited to illustrate the main resu...

Initial - Boundary Value Problems for Parabolic Equations

Existence of solutions of boundary value problems for Caputo fractional differential equations on time scales

‎In this paper‎, ‎we study the boundary-value problem of fractional‎ ‎order dynamic equations on time scales‎, ‎$$‎ ‎^c{Delta}^{alpha}u(t)=f(t,u(t)),;;tin‎ ‎[0,1]_{mathbb{T}^{kappa^{2}}}:=J,;;1

Boundary value problems for higher order ordinary differential equations

Let f : [a, b] × R n+1 → R be a Carathéodory's function. Let {t h }, with t h ∈ [a, b], and {x h } be two real sequences. In this paper, the family of boundary value problems´x is considered. It is proved that these boundary value problems admit at least a solution for each k ≥ ν, where ν ≥ n + 1 is a suitable integer. Some particular cases, obtained by specializing the sequence {t h }, are poi...