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Exact solution for heat conduction inside a sphere with heat absorption using the regularized Hilfer-Prabhakar derivative
  • Hager Elhadedy,
  • Abass Abdel Kader,
  • Mohamed Abdel Latif
Hager Elhadedy
Mansoura University Faculty of Engineering
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Abass Abdel Kader
Mansoura University Faculty of Engineering
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Mohamed Abdel Latif
Mansoura University Faculty of Engineering

Corresponding Author:[email protected]

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Abstract

In this article, we utilize the finite Sine-Fourier transform (FSFT) and the Laplace transform (LT) for solving fractional partial differential equations with regularized Hilfer-Prabhakar derivative. These transforms are used to get analytical solutions for the time fractional heat conduction equation (TFHCE) with the regularized Hilfer-Prabhakar derivative and with heat absorption in spherical coordinates. Two cases of Dirichlet boundary conditions are considered with obtaining analytical solution in each case. The effect of the parameters of the regularized Hilfer-Prabhakar derivative on the heat transfer inside the sphere is discussed using some figures.