Semilinear Caputo time-fractional pseudo-parabolic equations

Initial time difference quasilinearization for Caputo Fractional Differential Equations

Correspondence: [email protected]. tr Department of Statistics, Gaziosmanpasa University, Tasliciftlik Campus, 60250 Tokat, Turkey Abstract This paper deals with an application of the method of quasilinearization by not demanding the Hölder continuity assumption of functions involved and by choosing upper and lower solutions with initial time difference for nonlinear Caputo fractional different...

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

Optimal Control of Nonsmooth, Semilinear Parabolic Equations

This paper is concerned with an optimal control problem governed by a semilinear, nonsmooth operator differential equation. The nonlinearity is locally Lipschitz-continuous and directionally differentiable, but not Gâteaux-differentiable. Two types of necessary optimality conditions are derived, the first one by means of regularization, the second one by using the directional differentiability ...

Determining nodes for semilinear parabolic equations

We discuss the uniqueness of the equilibria of time-global solutions of general semilinear parabolic equations by a finite set of values of these solutions. More precisely, if the asymptotic behaviour of a time-global solution is known on an appropriate finite set, then the asymptotic behaviour of a time-global solution itself is entirely determined in a domain.

Heteroclinic orbits of semilinear parabolic equations