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1 pages, 204 KiB

Open AccessEditorial

Fractional Calculus in Mexico: The 5th Mexican Workshop on Fractional Calculus (MWFC)

by Jorge M. Cruz-Duarte and Porfirio Toledo-Hernández

Comput. Sci. Math. Forum 2022, 4(1), 7; https://doi.org/10.3390/cmsf2022004007 - 03 Feb 2023

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The Mexican Workshop on Fractional Calculus (MWFC) is a bi-annual international workshop and the largest Latin American technical event in the field of fractional calculus in Mexico [...] Full article

(This article belongs to the Proceedings of The 5th Mexican Workshop on Fractional Calculus)

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6 pages, 763 KiB

Open AccessProceeding Paper

Fractional Approach to the Study of Damped Traveling Disturbances in a Vibrating Medium

by Fernando Olivar-Romero

Comput. Sci. Math. Forum 2022, 4(1), 1; https://doi.org/10.3390/cmsf2022004001 - 22 Nov 2022

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Abstract

The Cauchy problem of a time–space fractional partial differential equation which has as a particular case the damped wave equation is solved for the Dirac delta initial condition. The solution is obtained in terms of H-Fox functions and models the travel of a [...] Read more.

The Cauchy problem of a time–space fractional partial differential equation which has as a particular case the damped wave equation is solved for the Dirac delta initial condition. The solution is obtained in terms of H-Fox functions and models the travel of a disturbance in a vibrating medium. Full article

(This article belongs to the Proceedings of The 5th Mexican Workshop on Fractional Calculus)

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10 pages, 5437 KiB

Open AccessProceeding Paper

Dynamic Analysis for the Physically Correct Model of a Fractional-Order Buck-Boost Converter

by Daniel F. Zambrano-Gutierrez, Jorge M. Cruz-Duarte, Gerardo Humberto Valencia-Rivera, Ivan Amaya and Juan Gabriel Avina-Cervantes

Comput. Sci. Math. Forum 2022, 4(1), 2; https://doi.org/10.3390/cmsf2022004002 - 22 Nov 2022

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Abstract

This work proposes a fractional-order mathematical model of a Buck-Boost converter performing in continuous conduction mode. To do so, we employ the average duty-cycle representation in state space, driven by the nonadimensionalize approach to avoid unit inconsistencies in the model. We also consider [...] Read more.

This work proposes a fractional-order mathematical model of a Buck-Boost converter performing in continuous conduction mode. To do so, we employ the average duty-cycle representation in state space, driven by the nonadimensionalize approach to avoid unit inconsistencies in the model. We also consider a Direct Current (DC) analysis through the fractional Riemann–Liouville (R-L) approach. Moreover, the fractional order Buck-Boost converter model is implemented in the Matlab/Simulink setting, which is also powered by the Fractional-order Modeling and Control (FOMCON) toolbox. When modifying the fractional model order, we identify significant variations in the dynamic converter response from this simulated scenario. Finally, we detail how to achieve a fast dynamic response without oscillations and an adequate overshoot, appropriately varying the fractional-order coefficient. The numerical results have allowed us to determine that with the decrease of the fractional order, the model presents minor oscillations, obtaining an output voltage response six times faster with a significant overshoot reduction of 67%, on average. Full article

(This article belongs to the Proceedings of The 5th Mexican Workshop on Fractional Calculus)

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8 pages, 949 KiB

Open AccessProceeding Paper

Patterns in a Time-Fractional Predator–Prey System with Finite Interaction Range

by Guillermo Chacón-Acosta and Mayra Núñez-López

Comput. Sci. Math. Forum 2022, 4(1), 3; https://doi.org/10.3390/cmsf2022004003 - 07 Dec 2022

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Abstract

Diffusive predator–prey systems are well known to exhibit spatial patterns obtained by using the Turing instability mechanism. reaction–diffusion systems were already studied by replacing the time derivative with a fractional order derivative, finding the conditions under which spatial patterns could be formed in [...] Read more.

Diffusive predator–prey systems are well known to exhibit spatial patterns obtained by using the Turing instability mechanism. reaction–diffusion systems were already studied by replacing the time derivative with a fractional order derivative, finding the conditions under which spatial patterns could be formed in such systems. The recent interest in fractional operators is due to the fact that many biological, chemical, physical, engineering, and financial systems can be well described using these tools. This contribution presents a diffusive predator–prey model with a finite interaction scale between species and introduces temporal fractional derivatives associated with species behaviors. We show that the spatial scale of the species interaction affects the range of unstable modes in which patterns can appear. Additionally, the temporal fractional derivatives further modify the emergence of spatial patterns. Full article

(This article belongs to the Proceedings of The 5th Mexican Workshop on Fractional Calculus)

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12 pages, 318 KiB

Open AccessProceeding Paper

Abelian Groups of Fractional Operators

by Anthony Torres-Hernandez, Fernando Brambila-Paz and Rafael Ramirez-Melendez

Comput. Sci. Math. Forum 2022, 4(1), 4; https://doi.org/10.3390/cmsf2022004004 - 19 Dec 2022

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Abstract

Taking into count the large number of fractional operators that have been generated over the years, and considering that their number is unlikely to stop increasing at the time of writing this paper due to the recent boom of fractional calculus, everything seems [...] Read more.

Taking into count the large number of fractional operators that have been generated over the years, and considering that their number is unlikely to stop increasing at the time of writing this paper due to the recent boom of fractional calculus, everything seems to indicate that an alternative that allows to fully characterize some elements of fractional calculus is through the use of sets. Therefore, this paper presents a recapitulation of some fractional derivatives, fractional integrals, and local fractional operators that may be found in the literature, as well as a summary of how to define sets of fractional operators that allow to fully characterize some elements of fractional calculus, such as the Taylor series expansion of a scalar function in multi-index notation. In addition, it is presented a way to define finite and infinite Abelian groups of fractional operators through a family of sets of fractional operators and two different internal operations. Finally, using the above results, it is shown one way to define commutative and unitary rings of fractional operators. Full article

(This article belongs to the Proceedings of The 5th Mexican Workshop on Fractional Calculus)

11 pages, 455 KiB

Open AccessProceeding Paper

Further Remarks on Irrational Systems and Their Applications

by Adrián-Josué Guel-Cortez, César-Fernando Méndez-Barrios, Diego Torres-García and Liliana Félix

Comput. Sci. Math. Forum 2022, 4(1), 5; https://doi.org/10.3390/cmsf2022004005 - 22 Dec 2022

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Abstract

Irrational Systems (ISs) are transfer functions that include terms with irrational exponents. Since such systems are ubiquitous and can be seen when solving partial differential equations, fractional-order differential equations, or non-linear differential equations; their nature seems to be strongly linked with a low-order [...] Read more.

Irrational Systems (ISs) are transfer functions that include terms with irrational exponents. Since such systems are ubiquitous and can be seen when solving partial differential equations, fractional-order differential equations, or non-linear differential equations; their nature seems to be strongly linked with a low-order description of distributed parameter systems. This makes ISs an appealing option for model-reduction applications and controls. In this work, we review some of the fundamental concepts behind a set of ISs that are of core importance in their stability analysis and control design. Specifically, we introduce the notion of multivalued functions, branch points, time response, and stability regions, as well as some practical applications where these systems can be encountered. The theory is accompanied by some numerical examples or simulations. Full article

(This article belongs to the Proceedings of The 5th Mexican Workshop on Fractional Calculus)

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5 pages, 653 KiB

Open AccessProceeding Paper

Analyzing All the Instances of a Chaotic Map to Generate Random Numbers

by Luis Gerardo de la Fraga

Comput. Sci. Math. Forum 2022, 4(1), 6; https://doi.org/10.3390/cmsf2022004006 - 18 Jan 2023

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Abstract

All possible configurations of a chaotic map without fixed points, called “nfp1”, in its implementation in fixed-point arithmetic are analyzed. As the multiplication on the computer does not follow the associative property, we analyze the number of forms in which the multiplications can [...] Read more.

All possible configurations of a chaotic map without fixed points, called “nfp1”, in its implementation in fixed-point arithmetic are analyzed. As the multiplication on the computer does not follow the associative property, we analyze the number of forms in which the multiplications can be performed in this chaotic map. As chaos enhanced the small perturbations produced in the multiplications, it is possible to built different pseudorandom number generators using the same chaotic map. Full article

(This article belongs to the Proceedings of The 5th Mexican Workshop on Fractional Calculus)

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