Journal of Mathematical Sciences: Advances and Applications[1] J. E. Warren and P. J. Root, The behavior of naturally fractured
reservoirs, Society of Petroleum Engineers Journal 3(03) (1963),
245-255.
DOI: https://doi.org/10.2118/426-PA
[2] J. Chang and Y. C. Yortsos, Pressure transient analysis of fractal
reservoirs, SPE Formation Evaluation 5(01) (1990), 31-38.
DOI: https://doi.org/10.2118/18170-PA
[3] R. Camacho Velazquez, G. Fuentes-Cruz and M. A. Vasquez-Cruz,
Decline-curve analysis of fractured reservoirs with fractal geometry,
SPE Reservoir Evaluation & Engineering 11(03) (2008), 606-619.
DOI: https://doi.org/10.2118/104009-PA
[4] R. Metzler, W. G. Glöckle and T. F. Nonnenmacher, Fractional
model equation for anomalous diffusion, Physica A: Statistical
Mechanics and its Applications 211(1) (1994), 13-24.
DOI: https://doi.org/10.1016/0378-4371(94)90064-7
[5] R. Camacho Velazquez, M. A. Vasquez-Cruz, R. Castrejon-Aivar and
V. Arana-Ortiz, Pressure transient and decline curve behaviors in
naturally fractured vuggy carbonate reservoirs, SPE Reservoir
Evaluation & Engineering 8(02) (2005), 95-112.
DOI: https://doi.org/10.2118/77689-PA
[6] T. Ertekin, Principles of Numerical Simulation of Oil Reservoirs:
An Overview, In Heavy Crude Oil Recovery, Springer, the Netherlands,
1984.
DOI: https://doi.org/10.1007/978-94-009-6140-1_11
[7] B. F. MartÃnez-Salgado, R. Rosas-Sampayo, A.
Torres-Hernández and C. Fuentes, Application of fractional calculus
to oil industry, Fractal Analysis: Applications in Physics,
Engineering and Technology (2017).
DOI: http://dx.doi.org/10.5772/intechopen.68571
[8] F. Brambila-Paz and A. Torres-Hernandez, Fractional Newton-Raphson
method, arXiv preprint (2017); arXiv: 1710.07634.
[9] F. Brambila-Paz, A. Torres-Hernandez, U. Iturrarán-Viveros and
R. Caballero-Cruz, Fractional Newton-Raphson method accelerated with
Aitken’s method, arXiv preprint (2018); arXiv:1804.08445.
[10] A. Torres-Hernandez, F. Brambila-Paz and E. De-la-Vega,
Fractional Newton-Raphson method and some variants for the solution of
nonlinear systems, Applied Mathematics and Sciences: An International
Journal 7(1) (2020), 13-27.
DOI: https://doi.org/10.5121/mathsj.2020.7102
[11] A. Torres-Hernandez, F. Brambila-Paz and P. M. Rodrigo, Reduction
of a nonlinear system and its numerical solution using a fractional
iterative method, arXiv preprint (2020); arXiv: 2007.02776.
[12] A. Torres-Hernandez, F. Brambila-Paz, P.M. Rodrigo and E.
De-La-Vega, Fractional pseudo-Newton method and its use in the
solution of a nonlinear system that allows the construction of a
hybrid solar receiver, Applied Mathematics and Sciences: An
International Journal 7(2) (2020), 1-12.
DOI: https://doi.org/10.5121/mathsj.2020.7201
[13] C. A. T. MartÃnez and F. Brambila-Paz, Numerical comparison
between RBF schemes with respect to other approaches to solve
fractional partial differential equations and their advantages when
choosing non-uniform nodes, Journal of Mathematics and Statistical
Science 5(5) (2019), 85-105.
[14] C. A. T. MartÃnez and C. Fuentes, Applications of radial basis
function schemes to fractional partial differential equations, Fractal
Analysis: Applications in Physics, Engineering and Technology
(2017).
DOI: http://dx.doi.org/10.5772/67892
[15] A. Le Mehaute, Transfer processes in fractal media, Journal of
Statistical Physics 36(5-6) (1984), 665-676.
DOI: https://doi.org/10.1007/BF01012930
[16] R. Raghavan and C. Chen, Fractional diffusion in rocks produced
by horizontal wells with multiple, transverse hydraulic fractures of
finite conductivity, Journal of Petroleum Science and Engineering 109
(2013), 133-143.
DOI: https://doi.org/10.1016/j.petrol.2013.08.027
[17] R. W. Holy, Numerical Investigation of 1D Anomalous Diffusion in
Fractured Nanoporous Reservoirs, PhD Dissertation, Colorado School of
Mines, Arthur Lake Library, 2016.
[18] Y. Hatano, J. Nakagawa, S. Wang and M. Yamamoto, Determination of
order in fractional diffusion equation, Journal of Math-for-Industry
5(A) (2013), 51-57.
[19] J. Bear, Dynamics of Fluids in Porous Media, Dover, 1988.
[20] D. W. Peaceman, Fundamentals of Numerical Reservoir Simulation,
1st Edition, Developments in Petroleum Science, Volume 6, Elsevier
Science, 1977.
[21] C. Fuentes, Informe VI. Fondo Sectorial
CONACYT-SENER-Hidrocarburos, Technical Report S0018-2011-11,
(2014).
[22] Rajagopal Raghavan and Chih-Cheng Chen, A conceptual structure to
evaluate wells producing fractured rocks of the Permian basin, In SPE
Annual Technical Conference and Exhibition, Society of Petroleum
Engineers, 2018.
DOI: https://doi.org/10.2118/191484-MS
[23] D. Baleanu, E. Diethelm K. Scalas and J. J. Trujillo, Fractional
Calculus, World Scientific, 2012.
[24] Urs Graf, Applied Laplace Transforms and z-Transforms for
Scientists and Engineers: A Computational Approach using a Mathematica
Package, Birkhäuser, 2012.
DOI: https://doi.org/10.1007/978-3-0348-7846-3
[25] Harald Stehfest, Algorithm 368: Numerical inversion of Laplace
transforms D5, Communications of the ACM 13(1) (1970), 47-49.
DOI: https://doi.org/10.1145/355598.362787
