Corrigendum: New numerical approach for fractional differential equations

Atangana, Abdon; Owolabi, Kolade M.

doi:10.1051/mmnp/2021039

Cited by 6 publications

(1 citation statement)

References 2 publications

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“…Many numerical techniques can be used to solve (43) [31,32]. In our case, we used the Adams-Bashford method [33] for partitioning the interval [0, T] into n equal subdivisions [t i , t i+1 ] with a width h = T/n, t i = ch for c = 0,1, .…”

Section: Numerical Solution Proceduresmentioning

confidence: 99%

Investigation of Egyptian Banks’ Competition through a Riesz–Caputo Fractional Model

2023

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In this paper, a four-dimensional competition model, driven by the Riesz-Caputo operator, is established. Then, the presented model’s uniqueness, existence, and stability are discussed. After that, the model is applied to describe the profit competition between Egyptian banks. Using the Hamiltonian definition of optimal control, we set a control strategy for banks’ profits during crises as a pre-step measure to counteract their negative impact. Finally, the model is solved numerically using an extended Adams–Bashford scheme. The valid data between the end of 2016 and 2020 are used for numerical simulations, while the data between the end of 2021 and 2022 are used for prediction measurements. From the results, it can be seen that the COVID-19 crisis resulted in a sudden decrease in banks’ profits during 2020, and if there were a control system enabled, it could have compensated for this decrease.

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Section: Numerical Solution Proceduresmentioning

confidence: 99%

Investigation of Egyptian Banks’ Competition through a Riesz–Caputo Fractional Model

2023

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Fractional‐order modeling of Chikungunya virus transmission dynamics

Chavada,

Pathak,

Khirsariya

2024

Math Methods in App Sciences

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This article presents two innovative mathematical models for the dynamics of Chikungunya virus contamination by using Caputo fractional derivative. By applying the recently developed numerical technique to find the approximate solutions for the Chikungunya virus system which allowing us for the valuable insights. Through a rigorous analysis of the obtained numerical and graphical solutions, the impact of fractional orders on the infection dynamics is thoroughly examined. Additionally, Banach's fix point theorm is used to investigates the existence, uniqueness, and stability properties of the solutions, providing a deeper understanding of the key parameters that affect the spread and persistence of the infection.

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Study of two-dimensional nonlinear coupled time-space fractional order reaction advection diffusion equations using shifted Legendre-Gauss-Lobatto collocation method

Anjuman,

Chopra,

Das

et al. 2024

Continuum Mech. Thermodyn.

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In this article, the nonlinear coupled two-dimensional space-time fractional order reaction-advection–diffusion equations (2D-STFRADEs) with initial and boundary conditions is solved by using Shifted Legendre-Gauss-Lobatto Collocation method (SLGLCM) with fractional derivative defined in Caputo sense. The SLGLC scheme is used to discretize the coupled nonlinear 2D-STFRADEs into the shifted Legendre polynomial roots to convert it to a system of algebraic equations. The efficiency and efficacy of the scheme are confirmed through error analysis while applying the scheme on two existing problems having exact solutions. The impact of advection and reaction terms on the solution profiles for various space and time fractional order derivatives are shown graphically for different particular cases. A drive has been made to study the convergence of the proposed scheme, which has been applied on the proposed mathematical model.

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Corrigendum: New numerical approach for fractional differential equations

Cited by 6 publications

References 2 publications

Investigation of Egyptian Banks’ Competition through a Riesz–Caputo Fractional Model

Investigation of Egyptian Banks’ Competition through a Riesz–Caputo Fractional Model

Fractional‐order modeling of Chikungunya virus transmission dynamics

Study of two-dimensional nonlinear coupled time-space fractional order reaction advection diffusion equations using shifted Legendre-Gauss-Lobatto collocation method

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