Wiener–Hopf technique for a fractional mixed boundary value problem in cylindrical layer

Abstract

Abstract In this paper, we study the heat transfer modeling during freezing of a biological tissue and present an analytical approach for solving the heat transfer problem in cryosurgery. We consider a time-fractional bio-heat equation in the cylindrical coordinate and employ the Wiener–Hopf technique to find the temperature of tissue in two different domains by the factorization of associated Wiener–Hopf kernel. We discuss the fundamental roles of the Bessel and Wright functions in determining the analytical solution of fractional cryosurgery problem.

Keywords

• 26A33
• 33C10
• 34A08
• 35R11
• 44A10