*Article* **Time-Fractional Heat Conduction in Two Joint Half-Planes**

### **Yuriy Povstenko 1,***∗* **and Joanna Klekot 2**


Received: 4 June 2019; Accepted: 14 June 2019; Published: 16 June 2019

**Abstract:** The heat conduction equations with Caputo fractional derivative are considered in two joint half-planes under the conditions of perfect thermal contact. The fundamental solution to the Cauchy problem as well as the fundamental solution to the source problem are examined. The Fourier and Laplace transforms are employed. The Fourier transforms are inverted analytically, whereas the Laplace transform is inverted numerically using the Gaver–Stehfest method. We give a graphical representation of the numerical results.

**Keywords:** fractional calculus; non-Fourier heat conduction; Caputo derivative; Fourier transform; Laplace transform
