A peculiar application of the fractal–fractional derivative in the dynamics of a nonlinear scabies model

Rashid, Saima; Kanwal, Bushra; Jarad, Fahd; Elagan, S. K.

doi:10.1016/j.rinp.2022.105634

Cited by 8 publications

(2 citation statements)

References 44 publications

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“…We investigate the effect of the order on neuronal activity by considering the parameter choice from the previous section. We first follow the traditional approach of linearizing the nonlinear system around the equilibrium solutions and study their corresponding stability (Amirian et al, 2020;Zafar et al, 2022;Azizi, 2022;Rashid et al, 2022). To do so, we recall traditional stability results of linear systems in the fractional-order case.…”

Section: Effect Of Cortical Disinhibition On Fractional-order Wilson-...mentioning

confidence: 99%

A fractional-order Wilson-Cowan formulation of cortical disinhibition

González-Ramírez

2023

Preprint

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This work presents a fractional-order Wilson-Cowan model derivation under Caputo’s formalism, considering an order of 0 < α ≤ 1. To that end, we propose memory-dependent response functions and average neuronal excitation functions that permit us to naturally arrive to a fractional-order model that incorporates past dynamics into the description of synaptically coupled neuronal populations' activity. We then focus on a particular example to analyze the fractional-order dynamics of the disinhibited cortex. This system mimics cortical activity during neurological disorders such as epileptic seizures, which allows brain dynamics to transition to a hyperexcited activity state. In the first-order mathematical model, we recover traditional results showing a transition from a low-level activity state to a plausibly pathological high-level activity state as an external factor modifies cortical inhibition. On the other hand, under the fractional-order formulation, we establish novel results showing that the system resists such transition as the order is decreased, permitting the possibility of staying in the low-activity state even with increased disinhibition. Furthermore, considering the memory index interpretation of the fractional-order model motivation here developed, our results establish that by increasing the memory index, the system becomes more resistant to transitioning towards the high-level activity state. That is, a possible effect of the memory index is to stabilize neuronal activity. To summarize our results, we present a two-parameter structural portrait describing the system’s dynamics dependent on a proposed disinhibition parameter and the order. We also explore numerical model simulations to validate our results.

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Section: Effect Of Cortical Disinhibition On Fractional-order Wilson-...mentioning

confidence: 99%

A fractional-order Wilson-Cowan formulation of cortical disinhibition

González-Ramírez

2023

Preprint

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“…Moreover, it is applied in the solution of linear constant coefficient fractional differential equations of any commensurate order and the CRONE control-system design tool-box for the control engineering community (see [19,20] and related references therein). Recently many researchers have made tremendous contributions to the topic of fractional calculus by developing multiple fractional expressions in diverse publications (see, for instance, [4,25,26,28,[30][31][32]). Also, its applications have been found in various fields of science and engineering, such as rheology, fluid flow, probability, and electrical networks.…”

Section: Introduction and Main Resulatsmentioning

confidence: 99%

Endpoint Estimates for Commutators of Fractional Integral Operators on the p-Adic Vector Space

Chang

2023

Preprint

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In this paper, the main aim is to prove the weak type L log L estimates for commutators of fractional integral operators and the higher order in the context of the p-adic version of Lebesgue spaces, where the symbols of the commutators belong to the p-adic version of BMO space, in addition, we also establish the estimates of the sharp function on the p-adic vector space. AMS(2020) Subject Classification: 42B35, 11E95, 26A33, 26D10

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A fractional-order Wilson-Cowan formulation of cortical disinhibition

González-Ramírez

2023

J Comput Neurosci

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A peculiar application of the fractal–fractional derivative in the dynamics of a nonlinear scabies model

Cited by 8 publications

References 44 publications

A fractional-order Wilson-Cowan formulation of cortical disinhibition

A fractional-order Wilson-Cowan formulation of cortical disinhibition

Endpoint Estimates for Commutators of Fractional Integral Operators on the p-Adic Vector Space

A fractional-order Wilson-Cowan formulation of cortical disinhibition

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