• Fractional Extensions of some Boundary Value Problems in Oil Strata

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      https://www.ias.ac.in/article/fulltext/pmsc/117/02/0267-0281

    • Keywords

       

      Laplace transform; Caputo differintegral operator; Efros’ theorem; Wright function; temperature field; auxiliary functions; convolution; fractional heat equation.

    • Abstract

       

      In the present paper, we solve three boundary value problems related to the temperature field in oil strata - the fractional extensions of the incomplete lumped formulation and lumped formulation in the linear case and the fractional generalization of the incomplete lumped formulation in the radial case. By using the Caputo differintegral operator and the Laplace transform, the solutions are obtained in integral forms where the integrand is expressed in terms of the convolution of some auxiliary functions of Wright function type. A generalization of the Laplace transform convolution theorem, known as Efros’ theorem is widely used.

    • Author Affiliations

       

      Mridula Garg1 Alka Rao1

      1. Department of Mathematics, University of Rajasthan, Jaipur 302 004, India
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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