Luis X. Vivas-Cruz

Luis X. Vivas-Cruz
Universidad Autónoma de Guerrero · Faculty of Mathematics

PhD
Development of algorithms with parallel computation for the numerical solution of fractional differential equations

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9
Publications
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38
Citations
Additional affiliations
September 2016 - December 2017
Center for Engineering and Industrial Development
Position
  • PhD Student

Publications

Publications (9)
Article
Full-text available
Fractional Partial Differential equations (FPDEs) are essential for modeling complex systems across various scientific and engineering areas. However, efficiently solving FPDEs presents significant computational challenges due to their inherent memory effects, often leading to increased execution times for numerical solutions. This study proposes a...
Article
Full-text available
We use the unified transform method (UTM) to solve initial‐boundary value problems for the fractional advection–diffusion‐type equation (FADE) on the real half line. We generalize this equation using the modified definition of the Atangana–Baleanu fractional derivative of order α∈(0,1]$$ \alpha \in \left(0,1\right] $$ in order to satisfy the initia...
Article
The performance of the hyperbolic-numerical inverse Laplace transform (hyperbolic-NILT) method is evaluated when it is used to solve time-fractional ordinary and partial differential equations. With this purpose, the formalistic fractionalization approach of Gompertz and diffusion equations are used as model problems, i.e., in the Gompertz and diff...
Article
Modeling of fluid flow considering radially symmetric reservoirs is common in groundwater science and petroleum engineering. The Hankel transform is suitable for solving boundary-value problems considering this flow geometry. However, there are few applications of this transform for reservoirs with a finite wellbore radius, despite there are formul...
Article
We obtain the exact analytic solutions of a fluid flow model that includes the Caputo-Fabrizio operator and new constitutive equations in its definition. Formulas are obtained for a slightly compressible fluid in an infinite single-porosity reservoir with the inner boundary having a constant pressure. The flow equation is given by $$ ^{CFC}_{\ \ \...
Preprint
The joint Laplace-Hankel transform is used in order to add new solutions of fluid flow in a fractured reservoir for applications in oilfield production or groundwater studies. We consider four cases resulting from the following combination of boundary conditions of a reservoir model: constant terminal pressure or constant terminal rate and constant...
Article
This work focuses mainly on the study of numerical solutions, which are obtained using the θ-method, of a generalized Warren and Root model that includes a second-order wave-like equation in its formulation. The solutions approximately describe the single-phase hydraulic head in fractures by considering the finite velocity of propagation by means o...
Article
Full-text available
We exactly solved a Warren and Root-like model that considers telegraphic fluid flow, a constant hydraulic head at the bottomhole, and an infinite Euclidean reservoir with radial flux. Complex integrals on the Bromwich contour are used to obtain the exact solutions of the hydraulic head and flux. Given that the behavior of the propagation of the hy...
Article
Full-text available
In this paper, we implement the Bayesian statistical inversion theory to obtain the solution for an inverse problem of growth data, using a fractional population growth model. We estimate the parameters in the model and we make a comparison between this model and an exponential one, based on an approximation of Bayes factor. A simulation study is c...

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