Fuzzy Type RK4 Solutions to Fuzzy Hybrid Retarded Delay Differential Equations

Dhandapani, Prasantha Bharathi; Băleanu, Dumitru; Thippan, T. Jayakumar; Sivakumar, V.

doi:10.3389/fphy.2019.00168

Cited by 10 publications

(7 citation statements)

References 15 publications

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“…Delay differential equations (DDEs): During the last few years, there have been many studies on DDEs. A very special type of retarded delay differential equations called fuzzy hybrid retarded equations are studied in [1]. For these equations, numerical schemes based on Runge-Kutta schemes are a good option to obtain accurate solutions.…”

Section: Analytical and Numerical Methods For Differential Equations And Applicationsmentioning

confidence: 99%

“…Thus, in this research topic, readers can find papers on varying numerical methods and applications.Delay differential equations (DDEs): During the last few years, there have been many studies on DDEs. A very special type of retarded delay differential equations called fuzzy hybrid retarded equations are studied in [1]. For these equations, numerical schemes based on Runge-Kutta schemes are a good option to obtain accurate solutions.Recent advances in stochastic or fractional ODEs and PDEs have been published in the last few years.…”

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confidence: 99%

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Editorial: Analytical and Numerical Methods for Differential Equations and Applications

Martín-Vaquero

Wade

Guirao

et al. 2021

Front. Appl. Math. Stat.

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Editorial on the Research Topic Analytical and Numerical Methods for Differential Equations and ApplicationsIn the last few decades, new mathematical problems and models, described by differential equations, have brought to light applications in many areas including Physics, Chemistry, Engineering, Biomedicine, and Economics, among others.This research topic shows the large amount of different types of differential equations, thus it contains a selection of papers with recent advances in subjects as different as delay differential equations, nonlinear partial differential equations (PDEs), studied analytically or numerically, or because of their applications, fractional PDEs, and q-differential equations, etc. We would like to thank all the contributors of this issue, and also the referees. They all worked hard to shed some light on these topics for young researchers who would like to investigate some of these areas. Thus, in this research topic, readers can find papers on varying numerical methods and applications.Delay differential equations (DDEs): During the last few years, there have been many studies on DDEs. A very special type of retarded delay differential equations called fuzzy hybrid retarded equations are studied in [1]. For these equations, numerical schemes based on Runge-Kutta schemes are a good option to obtain accurate solutions.Recent advances in stochastic or fractional ODEs and PDEs have been published in the last few years. In this special issue, researchers can find two papers on a fractional PDEs model by [2] and [3], solved numerically with different procedures.Many scientific papers study PDEs, their applications, and also analytical procedures to study their properties. Thus, an analytical solution of the Biswas-Arshed equation is obtained in [4]. This is a non-linear PDE with important applications in physics. In a similar topic, the variable-coefficient Heisenberg ferromagnetic spin chain (vcHFSC) equation is considered in [5]. This equation is also a nonlinear PDEs method, and it can be solved with Lie-algebra groups.However, many other nonlinear PDEs are transformed into large systems of nonlinear ordinary differential equations (ODEs), where efficient solvers are necessary. In some cases, these PDEs need to be solved in complex geometries, a recent approach is described in [6], where a new procedure to solve nonlinear parabolic PDEs in triangles is explained. But, in other cases, research groups focus their works on the applications of these PDEs such as in [7]. For example, many physical (such as the magneto-hydrodynamics [MHD] problem analyzed in [8]), industrial, or complex economical situations can be modeled by nonlinear PDEs. Chemistry is another very important area; in Awais-Kuman, the authors modelized the peristaltic flow

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Section: Analytical and Numerical Methods For Differential Equations And Applicationsmentioning

confidence: 99%

mentioning

confidence: 99%

Editorial: Analytical and Numerical Methods for Differential Equations and Applications

Martín-Vaquero

Wade

Guirao

et al. 2021

Front. Appl. Math. Stat.

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“…A notable example by Wang et al (2021) showcases the efficacy of machine learning in forecasting electric load in energy systems through the application of a Clifford fuzzy support vector machine [16]. In another stride, Dhandapani et al ( 2019) demonstrated the successful utilization of numerical methods to solve complex fuzzy systems [27]. These instances underscore the transformative potential of harmonizing algebraic modeling, data analysis, and machine learning to analyze, predict, and optimize LA-Semigroup behavior.…”

Section: Exploring Applications and Examples: Mathematical Modeling O...mentioning

confidence: 99%

“…By exploring the properties, relationships, and composition of roughness sets within LA-Semigroups, researchers have deepened their understanding of this field's fundamental characteristics [6,7,26]. Additionally, the integration of data analysis and machine learning perspectives has opened up new avenues for research, enabling the development of predictive models, optimization techniques, and decision-making processes related to LA-Semigroup operations [27]. These advancements provide valuable insights into the efficient utilization and enhancement of LA-Semigroups in various applications.…”

Section: Introductionmentioning

confidence: 99%

Exploring Roughness in Left Almost Semigroups and Its Connections to Fuzzy Lie Algebras

Assiry,

Baklouti

2023

Symmetry

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This paper explores the concept of Generalized Roughness in LA-Semigroups and its applications in various mathematical disciplines. We highlight the fundamental properties and structures of Generalized Roughness, examining its relationships with Fuzzy Lie Algebras, Order Theory, Lattice Structures, Algebraic Structures, and Categorical Perspectives. Moreover, we investigate the potential of mathematical modeling, optimization techniques, data analysis, and machine learning in the context of Generalized Roughness. Our findings reveal important results in Generalized Roughness, such as the preservation of roughness under the fuzzy equivalence relation and the composition of roughness sets. We demonstrate the significance of Generalized Roughness in the context of order theory and lattice structures, presenting key propositions and a theorem that elucidate its properties and relationships. Furthermore, we explore the applications of Generalized Roughness in mathematical modeling and optimization, highlighting the optimization of roughness measures, parameter estimation, and decision-making processes related to LA-Semigroup operations. We showcase how mathematical techniques can enhance understanding and utilization of LA-Semigroups in practical scenarios. Lastly, we delve into the role of data analysis and machine learning in uncovering patterns, relationships, and predictive models in Generalized Roughness. By leveraging these techniques, we provide examples and insights into how data analysis and machine learning can contribute to enhancing our understanding of LA-Semigroup behavior and supporting decision-making processes.

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“…For the solution of fuzzy Fredholm integral equations of the second kind, Ezzati and Ziari discussed an approach which is based on Bernstein polynomials [14]. Similarly to generalized differentiability of fuzzy differential equations, hybrid retarded delay differential equations were solved numerically by Runge-Kutta method [15,16]. For noninteger order, the interval differential equations were solved in [17].…”

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confidence: 99%

Solution of fuzzy singular integral equation with Abel’s type kernel using a novel hybrid method

Bushnaq

Ullah

et al. 2020

Adv Differ Equ

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In this paper, we are applying a novel analytical hybrid method to find the solution of a fuzzy Volterra Abel's integral equation of the second kind. The fuzzy number is used in its parametric form under which the fuzzy Volterra Abel's integral equation will be converted into a system of integral equations as in a crisp case. Moreover, to solve the general fuzzy Volterra integral equation with Abel's type kernel, and to show that the proposed method is efficient, a few accurate and simple examples are given for the demonstration of our results. MSC: Primary 45Exx; 45E10; secondary 47B35

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Fuzzy Type RK4 Solutions to Fuzzy Hybrid Retarded Delay Differential Equations

Cited by 10 publications

References 15 publications

Editorial: Analytical and Numerical Methods for Differential Equations and Applications

Editorial: Analytical and Numerical Methods for Differential Equations and Applications

Exploring Roughness in Left Almost Semigroups and Its Connections to Fuzzy Lie Algebras

Solution of fuzzy singular integral equation with Abel’s type kernel using a novel hybrid method

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