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Analysis of solutions of the 1D fractional Cattaneo heat transfer equation

Siedlecka Urszula, Ciesielski Mariusz

Journal of Applied Mathematics and Computational Mechanics

2021

Vol. 20, nr 4

87--98

In this paper, a solution of the single-phase lag heat conduction problem is presented. The research concerns the generalized 1D Cattaneo equation in a whole-space domain, where a second order time derivative is replaced by the fractional Caputo derivative. The Fourier-Laplace transform technique is used to determine a solution of the considered problem. The numerical inversion of the Laplace transforms is applied. The effect of the order of the fractional derivative on the temperature distribution is investigated.

On a linear-quadratic problem with Caputo derivative

Idczak D., Walczak S.

Opuscula Mathematica

2016

Vol. 36, no. 1

49--68

In this paper, we study a linear-quadratic optimal control problem with a fractional control system containing a Caputo derivative of unknown function. First, we derive the formulas for the differential and gradient of the cost functional under given constraints. Next, we prove an existence result and derive a maximum principle. Finally, we describe the gradient and projection of the gradient methods for the problem under consideration.