Fundamental Solutions to Fractional Heat Conduction in Two Joint Half-Lines Under Conditions of Nonperfect Thermal Contact

At the interface dividing two media, an area appears that has its own physical characteristics which differ from the properties of the bulk materials. The small width of the interface area permits considering this area as a two-dimensional median surface with the specified physical characteristics. The fundamental solutions to the Cauchy problem as well as to the source problem are considered for fractional heat conduction in two joint half-lines under conditions of nonperfect thermal contact. The specific example of classical heat conduction is also investigated.