Author

# Martín Patricio Árciga Alejandre

Bio: Martín Patricio Árciga Alejandre is an academic researcher from Autonomous University of Guerrero. The author has contributed to research in topics: Fractal & Plane (geometry). The author has an hindex of 3, co-authored 9 publications receiving 19 citations.

##### Papers

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TL;DR: In this article, the authors considered an initial boundary value problem for a stochastic evolution equation with Riesz-fractional spatial derivative and white noise on the half-line, where the Fokas method and Picard scheme were used to prove existence and uniqueness.

6 citations

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TL;DR: In this paper, a generalized Teodorescu operator is introduced to obtain the explicit solution of this problem for a very wide classes of regions, including those with a fractal boundary.

Abstract: This paper is devoted to study a fundamental system of equations in plane Linear Elasticity Theory, the two-dimensional Lame–Navier system. We rewrite them in a compressed form in terms of the Cauchy–Riemann operators and it allows us to solve a kind of Riemann problem for this system. A generalized Teodorescu operator, to be introduced here, provides the means for obtaining the explicit solution of this problem for a very wide classes of regions, including those with a fractal boundary.

4 citations

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TL;DR: In this article, a biquaternionic reformulation of a fractional monochromatic Maxwell system is proposed and some examples are given to illustrate the quaternionic fractional approach emerges in linear hydrodynamics and elasticity.

Abstract: In this work, we propose a biquaternionic reformulation of a fractional monochromatic Maxwell system. Additionally, some examples are given to illustrate how the quaternionic fractional approach emerges in linear hydrodynamics and elasticity.

3 citations

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TL;DR: This paper rewrite the famous Lame-Navier system in terms of the euclidean Dirac operator, which suggests a very natural generalization involving the so-called structural sets and implements algorithms to compute with such partial differential operators.

Abstract: This paper is devoted to a fundamental system of equations in Linear Elasticity Theory: the famous Lame-Navier system. The Clifford algebra language allows us to rewrite this system in terms of the euclidean Dirac operator, which at the same time suggests a very natural generalization involving the so-called structural sets. We are interested in finding some structures in the solutions of these generalized Lame-Navier systems. Using MATLAB we also implement algorithms to compute with such partial differential operators as well as to verify some theoretical results obtained in the paper.

3 citations

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TL;DR: In this paper, a generalized Teodorescu operator was introduced to solve the Lame-Navier system problem for a wide class of regions, including those with a fractal boundary.

Abstract: This paper is devoted to study a fundamental system of equations in plane Linear Elasticity Theory, the two-dimensional Lame-Navier system. We rewrite them in a compressed form in terms of the Cauchy-Riemann operators and it allows us to solve a kind of Riemann problem for this system. A generalized Teodorescu operator, to be introduced here, provides the means for obtaining the explicit solution of this problem for a very wide classes of regions, including those with a fractal boundary.

2 citations

##### Cited by

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TL;DR: Sokolnikoff's book as discussed by the authors differs greatly from Southwell, Timoshenko, and Love in spirit and content, and is symptomatic of the change in outlook of American mathematics over the past few decades.

Abstract: THE appearance of a treatise in English upon the mathematical theory of elasticity is an event the potential importance of which may be judged by the that the author, in his frequent suggestions for collateral reading, refers to only three such, those of Southwell, Timoshenko, and Love. In spirit and content Sokolnikoff}s book differs greatly from each and all of these. It may be described by a possible sub-title: “A pure mathematician surveys topics related to certain problems in the mathematical theory of elasticity”. It is symptomatic of the change in outlook of American mathematics over the past few decades. Mathematical Theory Of Elasticity Prof. I. S. Sokolnikoff with the collaboration of Asst. Prof. R. D. Speche. Pp. xi + 373. (New York and London: McGraw-Hill Book Co., Inc., 1946.) 22s. 6d.

552 citations

01 Jan 2016

TL;DR: Some basic problems of the mathematical theory of elasticity, but end up in infectious downloads because people cope with some infectious bugs inside their computer.

Abstract: Thank you for downloading some basic problems of the mathematical theory of elasticity. As you may know, people have search hundreds times for their favorite readings like this some basic problems of the mathematical theory of elasticity, but end up in infectious downloads. Rather than reading a good book with a cup of coffee in the afternoon, instead they cope with some infectious bugs inside their computer.

423 citations

01 Jan 2016

TL;DR: The mathematical foundations of elasticity is universally compatible with any devices to read and is available in the book collection an online access to it is set as public so you can download it instantly.

Abstract: Thank you very much for downloading mathematical foundations of elasticity. As you may know, people have search numerous times for their favorite books like this mathematical foundations of elasticity, but end up in infectious downloads. Rather than reading a good book with a cup of tea in the afternoon, instead they are facing with some infectious bugs inside their laptop. mathematical foundations of elasticity is available in our book collection an online access to it is set as public so you can download it instantly. Our digital library saves in multiple countries, allowing you to get the most less latency time to download any of our books like this one. Kindly say, the mathematical foundations of elasticity is universally compatible with any devices to read.

271 citations

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TL;DR: The unified transform method, also known as the Fokas method, is considered for solving partial differential equations of fractional order and the applicability is demonstrated by implementing it to solve a model fractional problem.

40 citations

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TL;DR: In this paper, the numerical solution of fractional stochastic delay differential equations driven by Brownian motion was studied, based on linear B-spline interpolation, and the proposed algorithm was shown to be robust to noise.

Abstract: This paper studies the numerical solution of fractional stochastic delay differential equations driven by Brownian motion. The proposed algorithm is based on linear B-spline interpolation. ...

34 citations