[HTML][HTML] Finite element approximation of optimal control problems governed by time fractional diffusion equation

Z Zhou, W Gong - Computers & Mathematics with Applications, 2016 - Elsevier
In this paper Galerkin finite element approximation of optimal control problems governed by
time fractional diffusion equations is investigated. Piecewise linear polynomials are used to …

Existence of solutions for nonlinear fractional q-difference integral equations with two fractional orders and nonlocal four-point boundary conditions

B Ahmad, JJ Nieto, A Alsaedi, H Al-Hutami - Journal of the Franklin Institute, 2014 - Elsevier
We investigate the existence of solutions for a nonlinear fractional q-difference integral
equation (q-variant of the Langevin equation) with two different fractional orders and …

Fractional optimal control problem for differential system with delay argument

GM Bahaa - Advances in difference equations, 2017 - Springer
In this paper, we apply the classical control theory to a fractional differential system in a
bounded domain. The fractional optimal control problem (FOCP) for differential system with …

Optimal control problem for variable-order fractional differential systems with time delay involving Atangana–Baleanu derivatives

GM Bahaa - Chaos, Solitons & Fractals, 2019 - Elsevier
Abstract The Optimal Control Problem (OCP) for variable-order fractional differential systems
with time delay is considered. The fractional time derivative is Atangana–Baleanu …

Fractional optimal control problem for differential system with control constraints

GM Bahaa - Filomat, 2016 - JSTOR
In this paper, the fractional optimal control problem for differential system is considered. The
fractional time derivative is considered in Riemann-Liouville sense. Constraints on controls …

Finite element approximation of optimal control problem governed by space fractional equation

Z Zhou, Z Tan - Journal of Scientific Computing, 2019 - Springer
In this paper we investigate finite element approximation of optimal control problem
governed by space fractional diffusion equation with control constraints. The control variable …

Fractional optimal control problem for variable-order differential systems

GM Bahaa - Fractional Calculus and Applied Analysis, 2017 - degruyter.com
In this paper, we apply the classical control theory to a variable order fractional differential
system in a bounded domain. The Fractional Optimal Control Problem (FOCP) for variable …

Fast tensor product solvers for optimization problems with fractional differential equations as constraints

S Dolgov, JW Pearson, DV Savostyanov… - Applied Mathematics and …, 2016 - Elsevier
Fractional differential equations have recently received much attention within computational
mathematics and applied science, and their numerical treatment is an important research …

Error analysis of fully discrete finite element approximations to an optimal control problem governed by a time-fractional PDE

M Gunzburger, J Wang - SIAM Journal on Control and Optimization, 2019 - SIAM
The optimality system is derived for an optimal control problem governed by a time-fractional
PDE. A fully discrete finite element method along with convolution quadrature for time …

Optimal controls for Riemann–Liouville fractional evolution systems without Lipschitz assumption

S Zhu, Z Fan, G Li - Journal of Optimization Theory and Applications, 2017 - Springer
In this paper, an evolution system with a Riemann–Liouville fractional derivative is proposed
and analyzed. With the help of a resolvent technique, a suitable concept of solutions to this …