Fractional extensions of some boundary value problems in oil strata

TL;DR

This paper develops fractional mathematical models for temperature distribution in oil strata, solving boundary value problems using advanced integral transforms and special functions to generalize classical formulations.

Contribution

It introduces fractional extensions of boundary value problems in oil strata, employing Caputo derivatives and Efros' theorem for analytical solutions in integral form.

Findings

Solutions expressed via Wright functions and convolutions

Generalized classical models with fractional calculus

Analytical solutions in integral form

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.