A complex fractional mathematical modeling for the love story of Layla and Majnun

Kumar, Pushpendra; Ertürk, Vedat Suat; Murillo‐Arcila, Marina

doi:10.1016/j.chaos.2021.111091

Cited by 42 publications

(10 citation statements)

References 33 publications

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“…The model (4) has been shown positive results whenever the value of ω is decreased gradually from 1. [18,29,41,22,23,25].…”

Section: Discussionmentioning

confidence: 99%

“…The phenomenon of fractional order is more realistic as it incorporates the concept of non-integer models, which has been omitted in classical theory. P. Kumar et al [25] investigated a complex fractional mathematical modelling for Layla's love story, while A. Singh et al [37] discussed the complex dynamics of a discrete fractionalorder Leslie-Gower predator-prey model. A wide range of dynamics for different parameters is also discussed in their model and observed that the fractional-order parameter has a major effect on the stability of the system.…”

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confidence: 99%

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Stability analysis of fractional order modelling of social media addiction

Malik

Deepika

2023

MFC

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<p style='text-indent:20px;'>In this article, we explored the fractional order mathematical modelling of social media addiction. For the fractional order model of social media addiction, the free equilibrium point <inline-formula><tex-math id="M1">\begin{document}$ E_{0} $\end{document}</tex-math></inline-formula>, endemic equilibrium point <inline-formula><tex-math id="M2">\begin{document}$ E_{*} $\end{document}</tex-math></inline-formula>, and basic reproduction number <inline-formula><tex-math id="M3">\begin{document}$ R_0 $\end{document}</tex-math></inline-formula> have been found. We discussed the stability analysis of the order model of social media addiction through the next generation matrix and fractional Routh-Hurwitz criterion. We also explained the fractional order mathematical modelling of social media addiction by applying a highly reliable and efficient scheme known as q-Homotopy Analysis Sumudu Transformation Method (q-HASTM). This technique q-HASTM is the hybrid scheme based on q-HAM and Sumudu transform technique. In the end, the numerical simulation of the fractional order model of social media addiction is also explained by using the generalized Adams-Bashforth-Moulton method.</p>

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“…The model (4) has been shown positive results whenever the value of ω is decreased gradually from 1. [18,29,41,22,23,25].…”

Section: Discussionmentioning

confidence: 99%

mentioning

confidence: 99%

Stability analysis of fractional order modelling of social media addiction

Malik

Deepika

2023

MFC

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“…In [ 20 ], authors have studied the dynamics of cancer therapy by using the Caputo-type time-delay system. Kumar et al [ 21 ] have discussed a complex fractional-order model for describing the love story of a couple. Kumar et al [ 22 ] have explored the outbreaks of Covid-19 in Argentina by using the daily reported cases.…”

Section: Introductionmentioning

confidence: 99%

A study on the dynamics of alkali–silica chemical reaction by using Caputo fractional derivative

Kumar¹,

Govindaraj²,

Ertürk

et al. 2022

Pramana - J Phys

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In this paper, we propose a mathematical study to simulate the dynamics of alkali–silica reaction (ASR) by using the Caputo fractional derivative. We solve a non-linear fractional-order system containing six differential equations to understand the ASR. For proving the existence of a unique solution, we use some recent novel properties of Mittag–Leffler function along with the fixed point theory. The stability of the proposed system is also proved by using Ulam–Hyers technique. For deriving the fractional-order numerical solution, we use the well-known Adams–Bashforth–Moulton scheme along with its stability. Graphs are plotted to understand the given chemical reaction practically. The main reason to use the Caputo-type fractional model for solving the ASR system is to propose a novel mathematical formulation through which the ASR mechanism can be efficiently explored. This paper clearly shows the importance of fractional derivatives in the study of chemical reactions.

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“…To date, fractional operators have been used in various scientific and engineering fields by using different kinds of mathematical modelings. Recently, fractional derivatives have been used in disease dynamics [15,16], mechanics [17], psychology [18], engineering [19], advanced modeling via fractal-fractional operators [20], etc. For the sake of the various advantages of fractional operators for memory effects, modeling dynamic systems using fractional calculus has been met with scepticism [21,22].…”

Section: Introductionmentioning

confidence: 99%

A Study on the 3D Hopfield Neural Network Model via Nonlocal Atangana–Baleanu Operators

et al. 2022

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Hopfield neural network (HNN) is considered as an artificial model derived from the brain structures and it is an important model that admits an adequate performance in neurocomputing. In this article, we solve a dynamical model of 3D HNNs via Atangana–Baleanu (AB) fractional derivatives. To find the numerical solution of the considered dynamical model, the well-known Predictor-Corrector (PC) method is used. A number of cases are taken by using two different sets of values of the activation gradient of the neurons as well as six different initial conditions. The given results have been perfectly established using the different fractional-order values on the given derivative operator. The objective of this research is to investigate the dynamics of the proposed HNN model at various values of fractional orders. Nonlocal characteristic of the AB derivative contains the memory in the system which is the main motivation behind the proposal of this research.

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A complex fractional mathematical modeling for the love story of Layla and Majnun

Cited by 42 publications

References 33 publications

Stability analysis of fractional order modelling of social media addiction

Stability analysis of fractional order modelling of social media addiction

A study on the dynamics of alkali–silica chemical reaction by using Caputo fractional derivative

A Study on the 3D Hopfield Neural Network Model via Nonlocal Atangana–Baleanu Operators

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