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In this paper, author’s study sub diffusion bio heat transfer model and developed explicit finite difference scheme for time fractional sub diffusion bio heat transfer equation by using caputo fabrizio fractional derivative. Also discussed conditional stability and convergence of developed scheme. Furthermore numerical solution of time fractional sub diffusion bio heat transfer equation is obtained and it is represented graphically by Python.

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In the paper, we develop the Adomian Decomposition Method for fractional order nonlinear Kuramoto-Sivashinsky (KS) equation. Caputo fractional derivatives are used to define fractional derivatives. We know that KS equation has many applications in physical phenomenon such as reaction diffusion system, long waves on the boundary of two viscous fluids and hydrodynamics. In this paper, we will solve time fractional KS equation which may help to researchers for their work. We solve some examples numerically, which will show the efficiency and convenience of Adomian Decomposition Method.

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