Study on generalized fuzzy fractional human liver model with Atangana–Baleanu–Caputo fractional derivative

Verma, Lalchand; Meher, Ramakanta

doi:10.1140/epjp/s13360-022-03396-x

Cited by 13 publications

(4 citation statements)

References 32 publications

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“…The results show how accurate and useful the proposed method is for estimating the HIV model's solutions. The purpose of the research presented in [37] was to create a new fuzzy fractional model for the human liver. This model would incorporate the ABC fractional differentiability, which is also referred to as the ABC gH-differentiability.…”

Section: Introductionmentioning

confidence: 99%

Construction of a Computational Scheme for the Fuzzy HIV/AIDS Epidemic Model with a Nonlinear Saturated Incidence Rate

Arif,

Abodayeh,

Nawaz

2024

CMES

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This work aimed to construct an epidemic model with fuzzy parameters. Since the classical epidemic model does not elaborate on the successful interaction of susceptible and infective people, the constructed fuzzy epidemic model discusses the more detailed versions of the interactions between infective and susceptible people. The next-generation matrix approach is employed to find the reproduction number of a deterministic model. The sensitivity analysis and local stability analysis of the system are also provided. For solving the fuzzy epidemic model, a numerical scheme is constructed which consists of three time levels. The numerical scheme has an advantage over the existing forward Euler scheme for determining the conditions of getting the positive solution. The established scheme also has an advantage over existing non-standard finite difference methods in terms of order of accuracy. The stability of the scheme for the considered fuzzy model is also provided. From the plotted results, it can be observed that susceptible people decay by rising interaction parameters.

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Section: Introductionmentioning

confidence: 99%

Construction of a Computational Scheme for the Fuzzy HIV/AIDS Epidemic Model with a Nonlinear Saturated Incidence Rate

Arif,

Abodayeh,

Nawaz

2024

CMES

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“…The nonlocality of this derivative makes the future behavior of a dynamical system modeled with this derivative dependent on the current behavior and all its past behaviors. The interested reader can refer to previous research [34][35][36] to see some recent applications of this fractional derivative. In this article, we use this fractional derivative to introduce a new class of stochastic fractional IDEs and propose a numerical method for solving them.…”

Section: Introductionmentioning

confidence: 99%

A projection method based on the piecewise Chebyshev cardinal functions for nonlinear stochastic ABC fractional integro‐differential equations

Heydari,

Zhagharian,

Cattani

2024

Math Methods in App Sciences

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In this study, the Atangana–Baleanu fractional derivative in the Caputo type (as a kind of non‐local and non‐singular derivative) is used to define a new class of stochastic fractional integro‐differential equations. A projection method (more precisely, a Galerkin approach) based on the piecewise Chebyshev cardinal functions is developed to solve these stochastic fractional equations. To construct this method, the operational matrices of fractional and stochastic integrals of these basis functions are obtained and used in the established method. By approximating the solution of the problem with a finite expansion of the expressed basis functions (in which the expansion coefficients are unknown), a system of algebraic equations is obtained. By solving this system, the expansion coefficients and subsequently the solution of the original stochastic fractional problem are obtained. The convergence analysis of the proposed method is investigated, theoretically and numerically. The accuracy of the established procedure is illustrated by solving several numerical examples.

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“…To simulate a wide range of physical processes, numerous mathematical models used the ABC order operator of fractional order such as Allahviranloo and Ghanbari [32] examined the ABC fractional derivative to address the modification of fuzzy FDEs represented in parametric interval form. Verma and Meher [33] discussed the mathematical model of the human liver model in the fuzzy ABC sense. The fuzzy fractional differential equation investigated by Al-Smadi et al [34] using the ABC approach and the Mittag-Leffler kernel differential operator.…”

Section: Introductionmentioning

confidence: 99%

Numerical approach on time-fractional Sawada-Kotera equation based on fuzzy extension of generalized dual parametric homotopy algorithm

Al-Saedi,

Verma,

Meher

et al. 2024

Phys. Scr.

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‎This paper considers a fuzzy nonlinear fifth-order time-fractional Sawada-Kotera equation with a singular kernel and a non-singular Mittag-Leffler kernel‎. ‎The proposed fractional differential equation is discussed with the Caputo and ABC fractional derivative under strongly generalized results and with fuzzy modelling‎. ‎A novel double parametric approach‎, ‎i.e.‎, ‎q-homotopy analysis generalized transform method (q-HAGTM)‎, ‎is considered to find the solution of the proposed model with Caputo and ABC fractional derivatives‎. ‎The problem's uniqueness and convergence analysis are investigated using Banach's fixed point theorem‎. ‎Finally‎, ‎the numerical results have been validated by comparing them with the available results in Caputo and ABC sense under strongly generalized derivatives in the crisp case‎.

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Study on generalized fuzzy fractional human liver model with Atangana–Baleanu–Caputo fractional derivative

Cited by 13 publications

References 32 publications

Construction of a Computational Scheme for the Fuzzy HIV/AIDS Epidemic Model with a Nonlinear Saturated Incidence Rate

Construction of a Computational Scheme for the Fuzzy HIV/AIDS Epidemic Model with a Nonlinear Saturated Incidence Rate

A projection method based on the piecewise Chebyshev cardinal functions for nonlinear stochastic ABC fractional integro‐differential equations

Numerical approach on time-fractional Sawada-Kotera equation based on fuzzy extension of generalized dual parametric homotopy algorithm

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