An operational matrix based on the Independence polynomial of a complete bipartite graph for the Caputo fractional derivative

Baishya, Chandrali

doi:10.1007/s40324-021-00268-9

Cited by 11 publications

(8 citation statements)

References 49 publications

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“…The fractional calculus (FC) has long been regarded as a useful scientific tool for precisely expressing the classical memory and interaction of complex dynamic systems, events, or structures. Some applications of fractional calculus can be found in [21][22][23][24][25][26][27][28][29][30]. We also refer the readers to [31][32][33] for the stochastic modeling of anomalous diffusion.…”

Section: Tea Mosquito Bugmentioning

confidence: 99%

Dynamics of Fractional Model of Biological Pest Control in Tea Plants with Beddington–DeAngelis Functional Response

et al. 2021

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In this study, we depicted the spread of pests in tea plants and their control by biological enemies in the frame of a fractional-order model, and its dynamics are surveyed in terms of boundedness, uniqueness, and the existence of the solutions. To reduce the harm to the tea plant, a harvesting term is introduced into the equation that estimates the growth of tea leaves. We analyzed various points of equilibrium of the projected model and derived the conditions for the stability of these equilibrium points. The complex nature is examined by changing the values of various parameters and fractional derivatives. Numerical computations are conducted to strengthen the theoretical findings.

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Section: Tea Mosquito Bugmentioning

confidence: 99%

Dynamics of Fractional Model of Biological Pest Control in Tea Plants with Beddington–DeAngelis Functional Response

et al. 2021

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“…An operational matrix-based technique for the Caputo fractional system was presented in Ref. 22 . Spectral collocation methods are numerical techniques known for their accuracy and efficiency in solving different complex biological and mathematical differential systems.…”

Section: Introductionmentioning

confidence: 99%

Advanced stability analysis of a fractional delay differential system with stochastic phenomena using spectral collocation method

Xie,

Khan,

Sumelka

et al. 2024

Sci Rep

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In recent years, there has been a growing interest in incorporating fractional calculus into stochastic delay systems due to its ability to model complex phenomena with uncertainties and memory effects. The fractional stochastic delay differential equations are conventional in modeling such complex dynamical systems around various applied fields. The present study addresses a novel spectral approach to demonstrate the stability behavior and numerical solution of the systems characterized by stochasticity along with fractional derivatives and time delay. By bridging the gap between fractional calculus, stochastic processes, and spectral analysis, this work contributes to the field of fractional dynamics and enriches the toolbox of analytical tools available for investigating the stability of systems with delays and uncertainties. To illustrate the practical implications and validate the theoretical findings of our approach, some numerical simulations are presented.

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“…To determine the analytical solution to the linear and nonlinear FIDE and VIDE, A. S. Khan (3) has used a variation of parameter techniques. Numerous academics have recently worked on integro-differential equations and achieved superior results (4)(5)(6)(7)(8)(9)(10)(11) . The study of integral and IDEs, which contain two different types of integral operators, was the main emphasis of Hamoud and Ghadle (12) .…”

Section: Introductionmentioning

confidence: 99%

Numerical Solution of Non-linear Integro-differential Equations using Operational Matrix based on the Hosoya Polynomial of a Path Graph

Jayaprakasha¹,

Shashikumar²

2023

IJST

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Objectives: Introduction to new numerical techniques to solve differential, difference, and integro-differential equations (IDEs) are always remaining the thrust area of research for many scientists over the centuries. The prime objective of this work is to contribute a new numerical technique to solve IDEs. Method: To address non-linear integro-differential equations, we computed an operational matrix of derivatives based on the Hosoya polynomial of the path graph in this work. Findings: Using the derived operational matrix, we have solved both Volterra and Fredholm integrodifferential equations. Taking suitable examples accuracy of the projected method is demonstrated in this paper in terms of a graphical representation of the absolute error. The results of the examples reveal that the projected method is a suitable method to solve IDEs. Novelty: The application of the Hosoya polynomial of path graph to solve integro-differential equations is a novel approach in the field of numerical analysis.

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An operational matrix based on the Independence polynomial of a complete bipartite graph for the Caputo fractional derivative

Cited by 11 publications

References 49 publications

Dynamics of Fractional Model of Biological Pest Control in Tea Plants with Beddington–DeAngelis Functional Response

Dynamics of Fractional Model of Biological Pest Control in Tea Plants with Beddington–DeAngelis Functional Response

Advanced stability analysis of a fractional delay differential system with stochastic phenomena using spectral collocation method

Numerical Solution of Non-linear Integro-differential Equations using Operational Matrix based on the Hosoya Polynomial of a Path Graph

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