Reduce Differential Transform Method for Analytical Approximation of Fractional Delay Differential Equation

Naseem, Tahir

doi:10.54938/ijemdm.2022.01.2.35

Cited by 3 publications

(4 citation statements)

References 29 publications

(33 reference statements)

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“…Now, we can employ the rule (19) to the function y(x) = e x 2 (1−ς 2 ) h(ςx). Then, y(µ) will have singularities farther from the x-axis as compared to the singularities of h(µ), and this may improve the accuracy.…”

Section: Conflicts Of Interestmentioning

confidence: 99%

“…In [18], the authors solved a class of FDDEs including Liouville-Caputo fractional operator using the orthogonal Chelyshkov functions. Naseem et al [19] used the differential transform method for the analytical approximation of FDDE. Rebenda and Šmarda [20] used a differential transformation approach for solving functional differential equations with multiple delays.…”

Section: Introductionmentioning

confidence: 99%

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Numerical Solution of the Linear Fractional Delay Differential Equation Using Gauss–Hermite Quadrature

Aljawi,

Aljohani,

Kamran

et al. 2024

Symmetry

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Fractional order differential equations often possess inherent symmetries that play a crucial role in governing their dynamics in a variety of scientific fields. In this work, we consider numerical solutions for fractional-order linear delay differential equations. The numerical solution is obtained via the Laplace transform technique. The quadrature approximation of the Bromwich integral provides the foundation for several commonly employed strategies for inverting the Laplace transform. The key factor for quadrature approximation is the contour deformation, and numerous contours have been proposed. However, the highly convergent trapezoidal rule has always been the most common quadrature rule. In this work, the Gauss–Hermite quadrature rule is used as a substitute for the trapezoidal rule. Plotting figures of absolute error and comparing results to other methods from the literature illustrate how effectively the suggested approach works. Functional analysis was used to examine the existence of the solution and the Ulam–Hyers (UH) stability of the considered equation.

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Section: Conflicts Of Interestmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Numerical Solution of the Linear Fractional Delay Differential Equation Using Gauss–Hermite Quadrature

Aljawi,

Aljohani,

Kamran

et al. 2024

Symmetry

View full text Add to dashboard Cite

show abstract

“…The research content of this topic includes four modules: administrator, teacher, student, and independent [11]. The management system is divided into course management and user management.…”

Section: System Module Designmentioning

confidence: 99%

Nonlinear Differential Equation in University Education Information Course Selection System

Yangg,

Zhao

2023

Applied Mathematics and Nonlinear Sciences

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This paper applies a nonlinear differential equation to the information management system of college course selection. A teaching information management system based on an approximate learning strategy is presented by using statistical linearization technology. An imprecise controller is obtained by numerical simulation of Riccati differential equations with statistical linearization. This kind of Riccati differential equation differs significantly from the ordinary one. Then the system proposes a collaborative filtering method based on nonlinear differentiation based on student feature classification. At last, this paper systematically analyzes the differences between course selection systems, business recommendations, and student attributes—the system experiments on college students' choice of a learning platform. The study found that the method was correct 34.6% of the time. This system can provide practical guidance for students to choose courses.

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“…Nazam et al [20] established several results for generalized interpolative contractions. Naseem et al [21] worked on the analytical approximation of fractional delay differential equations.…”

Section: Introductionmentioning

confidence: 99%

Generalized Common Best Proximity Point Results in Fuzzy Metric Spaces with Application

et al. 2023

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The symmetry of fuzzy metric spaces has benefits for flexibility, ambiguity tolerance, resilience, compatibility, and applicability. They provide a more comprehensive description of similarity and offer a solid framework for working with ambiguous and imprecise data. We give fuzzy versions of some celebrated iterative mappings. Further, we provide different concrete conditions on the real valued functions J,S:(0,1]→R for the existence of the best proximity point of generalized fuzzy (J,S)-iterative mappings in the setting of fuzzy metric space. Furthermore, we utilize fuzzy versions of J,S-proximal contraction, J,S-interpolative Reich–Rus–Ciric-type proximal contractions, J,S-Kannan type proximal contraction and J,S-interpolative Hardy Roger’s type proximal contraction to examine the common best proximity points in fuzzy metric space. Also, we establish several non-trivial examples and an application to support our results.

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Reduce Differential Transform Method for Analytical Approximation of Fractional Delay Differential Equation

Cited by 3 publications

References 29 publications

Numerical Solution of the Linear Fractional Delay Differential Equation Using Gauss–Hermite Quadrature

Numerical Solution of the Linear Fractional Delay Differential Equation Using Gauss–Hermite Quadrature

Nonlinear Differential Equation in University Education Information Course Selection System

Generalized Common Best Proximity Point Results in Fuzzy Metric Spaces with Application

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