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Solution of fractional bioheat equations by finite difference method and HPM. (English) Zbl 1235.65113

Summary: We present a mathematical model of space-time fractional bioheat equation governing the process of heat transfer in tissues during thermal therapy. Using fractional backward finite difference scheme, the problem is converted into an initial value problem of vector-matrix form and homotopy perturbation method is used to solve it. Results are interpreted in the form of standard case and anomalous cases for taking different orders of space and time fractional derivatives.

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35R11 Fractional partial differential equations
35K20 Initial-boundary value problems for second-order parabolic equations
45K05 Integro-partial differential equations
92C50 Medical applications (general)
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