Series-form solutions of generalized fractional-fisher models with uncertainties using hybrid approach in Caputo sense

Qayyum, Mubashir; Tahir, Aneeza; Saeed, Syed Tauseef; Akgül, Ali

doi:10.1016/j.chaos.2023.113502

Cited by 10 publications

(2 citation statements)

References 34 publications

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“…• f ( ) a  f ( ) a for α ä[0,1] Definition 6. [44] For a real set , the fuzzy set  ˜is defined by a membership function…”

Section: Preliminariesmentioning

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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“…• f ( ) a  f ( ) a for α ä[0,1] Definition 6. [44] For a real set , the fuzzy set  ˜is defined by a membership function…”

Section: Preliminariesmentioning

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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“…Tese equations have many applications in various felds, such as fuid dynamics [14], kinetics [15], fnance [16], economics [17], and biology [18]. Fuzzy Volterra integrodiferential equations [19], fuzzy Fisher model [20], fuzzy population growth model [21], frst-order linear fuzzy differential equations [22], and fuzzy singular integrodiferential models [23] are some examples of fuzzy diferential equations.…”

Section: Introductionmentioning

confidence: 99%

Modeling and Analysis of the Fuzzy-Fractional Chaotic Financial System Using the Extended He–Mohand Algorithm in a Fuzzy-Caputo Sense

Qayyum,

Ahmad,

Tahir

et al. 2023

International Journal of Intelligent Systems

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This paper contains modeling of a fuzzy-fractional financial chaotic model based on triangular fuzzy numbers (TFNs) to predict the idea that long-term dependency and uncertainty both have an impact on the financial market. For solution purposes, the He–Mohand algorithm is proposed where homotopy perturbation is hybrid with Mohand transform in a fuzzy-Caputo sense. In analysis, solutions and corresponding errors at upper and lower bounds are estimated. The obtained numerical results are displayed in tables to show the reliability and efficiency of the proposed methodology. Upper bound errors range from 10 − 6 to 10 − 12 and lower bound errors from 10 − 6 to 10 − 11 . For graphical analysis, system profiles are illustrated as two-dimensional and three-dimensional plots at diverse values of fractional parameters and time to comprehend the physical behavior of the proposed fuzzy-fractional model. These plots demonstrate that the interest rate, price index, and investment demand decrease with the increase of the value of the r -cut at the lower bound. At the upper bound, this behavior is totally opposite. The chaotic behavior of the system at smaller values of saving rate, elasticity of demands, and per-investment cost is greater in contrast to their larger value. Analysis reveals that the proposed methodology (He–Mohand algorithm) provides a new way of understanding the complicated structure of financial systems and provides new insights into the dynamics of financial markets. This algorithm has potential applications in risk management, portfolio optimization, and trading strategies.

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Mathematical Modeling of Cancer Tumor Dynamics with Multiple Fuzzification Approaches in Fractional Environment

Qayyum,

Tahir

2023

Interdisciplinary Cancer Research

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Series-form solutions of generalized fractional-fisher models with uncertainties using hybrid approach in Caputo sense

Cited by 10 publications

References 34 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

Modeling and Analysis of the Fuzzy-Fractional Chaotic Financial System Using the Extended He–Mohand Algorithm in a Fuzzy-Caputo Sense

Mathematical Modeling of Cancer Tumor Dynamics with Multiple Fuzzification Approaches in Fractional Environment

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