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Reconstruct the Heat Conduction Model with Memory Dependent Derivative
Research Institute for ESMD Method and Its Applications, College of Science, Qingdao University of Technology, Qingdao, China
Research Institute for ESMD Method and Its Applications, College of Science, Qingdao University of Technology, Qingdao, China
- 1 Research Institute for ESMD Method and Its Applications, College of Science, Qingdao University of Technology, Qingdao, China
- 2 Research Institute for ESMD Method and Its Applications, College of Science, Qingdao University of Technology, Qingdao, China
Applied Mathematics·Volume 09 (2018)·Pages 1072–1080·Published 17 September 2018·DOI10.4236/am.2018.99072
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Abstract
The classical heat conduction equation is derived from the assumption that the temperature increases immediately after heat transfer, but the increase of temperature is a slow process, so the memory-dependent heat conduction model has been reconstructed. Numerical results show that the solution of the initial boundary value problem of the new model is similar to that of the classical heat conduction equation, but its propagation speed is slower than that of the latter. In addition, the propagation speed of the former is also affected by time delay and kernel function.
KeywordsPartial Differential EquationBoundary Value ProblemMemory-Dependent Derivative (MDD)Caputo Type Fractional DerivativeHeat Conduction Equation
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