Fractional heat conduction with heat absorption in a sphere under Dirichlet boundary condition

Journal Article · Sat Sep 15 04:00:00 EDT 2018 · Computational and Applied Mathematics

DOI:https://doi.org/10.1007/S40314-018-0585-7· OSTI ID:22769234

Povstenko, Yuriy ^[1]; Klekot, Joanna ^[2]

---

1. Jan Długosz University in Czȩstochowa, Institute of Mathematics and Computer Science, Faculty of Mathematics and Natural Sciences (Poland)
2. Czȩstochowa University of Technology, Institute of Mathematics, Faculty of Mechanical Engineering and Computer Science (Poland)

The time-fractional heat conduction equation with the Caputo derivative and with heat absorption term proportional to temperature is considered in a sphere in the case of central symmetry. The fundamental solution to the Dirichlet boundary value problem is found, and the solution to the problem under constant boundary value of temperature is studied. The integral transform technique is used. The solutions are obtained in terms of series containing the Mittag-Leffler functions being the generalization of the exponential function. The numerical results are illustrated graphically.

• OSTI ID: 22769234
• Journal Information: Computational and Applied Mathematics, Journal Name: Computational and Applied Mathematics Journal Issue: 4 Vol. 37; ISSN 0101-8205
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
BOUNDARY CONDITIONS
DIRICHLET PROBLEM
FOURIER TRANSFORMATION
LAPLACE TRANSFORMATION
MATHEMATICAL SOLUTIONS
SYMMETRY
THERMAL CONDUCTION