Abstract
Abstract In this study, we present some new results for the time fractional mixed boundary value problems. We consider a generalization of the Heat - conduction problem in two dimensions that arises during the manufacturing of p - n junctions. Constructive examples are also provided throughout the paper. The main purpose of this article is to present mathematical results that are useful to researchers in a variety of fields.
Highlights
Fractional partial differential equations provide an excellent model for the description of memory and hereditary properties of various processes and materials
This is the main advantage of fractional partial differential equations in comparison with classical integer - order models, in which such effects are neglected
Let us consider the following two-dimensional heat conduction problem that arises during the manufacture of p-n junctions
Summary
Fractional partial differential equations provide an excellent model for the description of memory and hereditary properties of various processes and materials. This is the main advantage of fractional partial differential equations in comparison with classical integer - order models, in which such effects are neglected. It is well - known that the mixed boundary value problems occur in the theory of elasticity in connection with punching and crack problems. Most mixed boundary value problems are solved using integral transform method or separation of variables [7,13,14]. An alternative method of solving mixed boundary value problem involves Green’s function
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