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An integral relationship for a fractional one-phase Stefan problem

  • Sabrina Roscani EMAIL logo and Domingo Tarzia

Abstract

A one-dimensional fractional one-phase Stefan problem with a temperature boundary condition at the fixed face is considered by using the Riemann–Liouville derivative. This formulation is more convenient than the one given in Roscani and Santillan (Fract. Calc. Appl. Anal., 16, No 4 (2013), 802–815) and Tarzia and Ceretani (Fract. Calc. Appl. Anal., 20, No 2 (2017), 399–421), because it allows us to work with Green’s identities (which does not apply when Caputo derivatives are considered). As a main result, an integral relationship between the temperature and the free boundary is obtained which is equivalent to the fractional Stefan condition. Moreover, an exact solution of similarity type expressed in terms of Wright functions is also given.

Acknowledgments

The present work has been sponsored by the Projects PIP N 0275 from CONICET–Univ. Austral, and by AFOSR–SOARD Grant FA9550 − 14 − 1 − 0122.

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Received: 2017-05-26
Published Online: 2018-10-29
Published in Print: 2018-08-28

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