A peculiar application of Atangana–Baleanu fractional derivative in neuroscience: Chaotic burst dynamics

Goufo, Emile Franc Doungmo; Mbehou, M.; Pene, Morgan M. Kamga

doi:10.1016/j.chaos.2018.08.003

Cited by 39 publications

(7 citation statements)

References 19 publications

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“…Moreover, a relationship established between fractional and fractal calculus. However the application of Atangana Balenue Fractal derivatives in neuroscience has been considered [10]. The qualitative theory of fraction DE in CFD,s very recent.…”

Section: Introductionmentioning

confidence: 99%

Existence Theory and Stability Analysis to a Class of Hybrid Differential Equations using Confirmable Fractal Fractional Derivative

Khan

2024

J Frac Calc & Nonlinear Sys

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This research work is related to study a class of hybrid differential equations (HDEs) using conformablefractal-fractional derivative (CFFD). Fixed point theory, in particular Krasnoselskii’s fixed point theoremis implemented on the said problem to establish the conditions for which there exists at least one solution.Also, stability results of Ulam-Hyers (U-H) and U-H Rassias types are derived. At the end of the paper, weadded examples for the purpose of justification and strengthen of our derived results.

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Section: Introductionmentioning

confidence: 99%

Existence Theory and Stability Analysis to a Class of Hybrid Differential Equations using Confirmable Fractal Fractional Derivative

Khan

2024

J Frac Calc & Nonlinear Sys

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“…For instance, Atangana 27 applied the Caputo–Fabrizio derivative to Fisher's reaction‐diffusion phenomenon and performed numerical simulations by using an iterative scheme. Goufo et al 28 explicated neuronal dynamics of the three‐dimensional Hindmarsh–Rose neuron model by operating the Atangana–Baleanu fractional derivative. Qureshi and Yusuf 29 utilized the least‐squares approach with experimental statistics to conduct a fractional comparative analysis of the chickenpox virus.…”

Section: Introductionmentioning

confidence: 99%

Fractional analysis of radiative blood transport through a porous channel containing multishaped cobalt nanoparticles: An application to hemodynamics

et al. 2023

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In this work, impacts of dispersing nonspherical shaped cobalt nanoparticles in the blood are analyzed for magnetohydrodynamic radiative transport of blood inside a vertical porous channel. An Oldroyd-B model is used to feature flow characteristics of blood along with Fourier's principle of heat transmission for the mathematical modeling of the problem. A fractional system is constructed by employing the idea of the Caputo-Fabrizio derivative on subsequent differential equations. The Laplace transform method is adopted to solve the fractional flow and energy equations subject to generalized boundary conditions, which involve time-dependent functions h τ ( ) and g τ ( ), respectively.Instead of promoting the analytic velocity and energy expressions, Zakian's numerical algorithm is operated to achieve the reverse transformation purpose of Laplace domain functions. To certify the obtained solutions, two additional numerical algorithms named Stehfest's algorithm and Durbin's algorithm are inculcated in this study, and comparative illustrations are drawn. For the extensive investigation of shear stress and heat transfer phenomenon, numerical simulations for the coefficient of skin friction and Nusselt number

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“…in 2019 [20] H. Kumar given A class of two variables sequence of functions satisfying Abel's integral equation and the phase shifts. In literature we can see many generalizations of Atangana-Baleanu fractional derivative like AB -derivative [13], AB derivative via MHD channel flow [34], AB RL type [12], we can see more [8,9,11,16,17,18,21,22,26,29,31,32,34,35]. Here we recollecting the definition of Atangana-Baleanu fractional integral, Let ω ∈ (0, 1] and integral define as,…”

Section: Introductionmentioning

confidence: 99%

Application of Fixed Point Theorem in the Solution of Integro-Differential Equations: A Complex Valued Approach

Shinde,

Pathak

2023

jnanabha

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It's remarkable to note that Complex valued Integro-differential and integral type equations are currently intensifying the attention of appreciable researchers due to their comprehensive applications. Thus, this study is fully devoted to the application part of the complex valued controlled, double controlled metric ∂c. We introduce an extended version of the Fisher and Banach type contraction theorem and present some examples to sustain our results. As part of the main theorem's application, we address a common solution with uncertainty in two different folds as follows: [I] Applying the fractional Adams-Bashforth method to the (1.1) FVIdE. [II] Applying it to the integral type equation (1.2) in the setting of the Extended complex valued metric space.

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A peculiar application of Atangana–Baleanu fractional derivative in neuroscience: Chaotic burst dynamics

Cited by 39 publications

References 19 publications

Existence Theory and Stability Analysis to a Class of Hybrid Differential Equations using Confirmable Fractal Fractional Derivative

Existence Theory and Stability Analysis to a Class of Hybrid Differential Equations using Confirmable Fractal Fractional Derivative

Fractional analysis of radiative blood transport through a porous channel containing multishaped cobalt nanoparticles: An application to hemodynamics

Application of Fixed Point Theorem in the Solution of Integro-Differential Equations: A Complex Valued Approach

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