Some properties and stability of Helmholtz model involved with nonlinear fractional difference equations and its relevance with quadcopter

Sivashankar, M.; Sabarinathan, S.; Nisar, Kottakkaran Sooppy; Ravichandran, C.; Kumar, B. V. Senthil

doi:10.1016/j.chaos.2023.113161

Cited by 20 publications

(8 citation statements)

References 22 publications

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“…Many researchers are focused on studying the dynamics such as complexity, stability, chaos, synchronization, and bifurcation of fractional differential models. Sivashankar et al [9] studied the stability of non-linear fractional Helmholtz model. Qayyum et al [10] fractionally modeled and simulated squeezing of nanofluid through He-Laplace algorithm.…”

Section: Introductionmentioning

confidence: 99%

Time-fractional lorenz type chaotic systems with asymmetric gaussian uncertainty: series solutions via extended He-Mohand algorithm in fuzzy-caputo sense

Qayyum,

Ahmad

2024

Phys. Scr.

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In this paper, modeling and analysis of 3D fuzzy-fractional Lorenz type systems is presented. System under-consideration includes classical Lorenz, Chen and Burke-Shaw chaotic systems. Asymmetrical Gaussian fuzzy logic with fractional calculus is applied to model complex systems with intricate patterns. The focus of this study is fuzzy-fractional modeling and simulations. For solution purpose, a hybrid perturbation method is introduced where standard homotopy perturbation method (HPM) is enhanced by incorporating Mohand transform in fuzzy-Caputo sense. This hybrid mechanism provides an efficient way to find solutions in fuzzy-fractional environment. Validity of obtained solutions is checked by computing residual errors, which ultimately confirms the convergence of applied methodology. The dynamical behavior of fuzzy-fractional chaotic models is analyzed through various 2-3D plots to represent the chaotic regions as well unpredictable trajectories at both upper and lower bounds. Fuzzy membership functions of 3D models at different values of fractional derivative are also demonstrated through 2D plots. Analysis reveals that extended hybrid methodology proves to be a valuable tool for researchers dealing with nonlinear chaotic fractional systems with fuzzy characteristics.

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Section: Introductionmentioning

confidence: 99%

Time-fractional lorenz type chaotic systems with asymmetric gaussian uncertainty: series solutions via extended He-Mohand algorithm in fuzzy-caputo sense

Qayyum,

Ahmad

2024

Phys. Scr.

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“…The new approaches and techniques developed in the field of Ulam-Hyers stability in differential equations find a lot of applications in other areas such as physics, electronics, biology, economics, mechanics, etc. [5][6][7]. The stability of functional equations is studied in [8] and the application of parallel electrical circuits.…”

Section: Introductionmentioning

confidence: 99%

Ulam–Hyers Stability of Linear Differential Equation with General Transform

Pinelas,

Selvam,

Sabarinathan

2023

Symmetry

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The main aim of this study is to implement the general integral transform technique to determine Ulam-type stability and Ulam–Hyers–Mittag–Leffer stability. We are given suitable examples to validate and support the theoretical results. As an application, the general integral transform is used to find Ulam stability of differential equations arising in Thevenin equivalent electrical circuit system. The results are graphically represented, which provides a clear and thorough explanation of the suggested method.

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“…Aziz Khan et al 24 studied that COVID-19 disease spreads from person to person with the help of the nabla Atangana-Baleanu-Caputo fractional derivative of Ulam-Hyers stability and optimal control strategies. In recent years, many researchers have studied the fractional model of Ulam stability with fractional results and related papers (see also 25 – 30 ).…”

Section: Introductionmentioning

confidence: 99%

Ulam-Hyers stability of tuberculosis and COVID-19 co-infection model under Atangana-Baleanu fractal-fractional operator

Selvam

Sabarinathan

Kumar

et al. 2023

Sci Rep

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The intention of this work is to study a mathematical model for fractal-fractional tuberculosis and COVID-19 co-infection under the Atangana-Baleanu fractal-fractional operator. Firstly, we formulate the tuberculosis and COVID-19 co-infection model by considering the tuberculosis recovery individuals, the COVID-19 recovery individuals, and both disease recovery compartment in the proposed model. The fixed point approach is utilized to explore the existence and uniqueness of the solution in the suggested model. The stability analysis related to solve the Ulam-Hyers stability is also investigated. This paper is based on Lagrange’s interpolation polynomial in the numerical scheme, which is validated through a specific case with a comparative numerical analysis for different values of the fractional and fractal orders.

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Some properties and stability of Helmholtz model involved with nonlinear fractional difference equations and its relevance with quadcopter

Cited by 20 publications

References 22 publications

Time-fractional lorenz type chaotic systems with asymmetric gaussian uncertainty: series solutions via extended He-Mohand algorithm in fuzzy-caputo sense

Time-fractional lorenz type chaotic systems with asymmetric gaussian uncertainty: series solutions via extended He-Mohand algorithm in fuzzy-caputo sense

Ulam–Hyers Stability of Linear Differential Equation with General Transform

Ulam-Hyers stability of tuberculosis and COVID-19 co-infection model under Atangana-Baleanu fractal-fractional operator

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