On the solution of the endolymph equation using fractional calculus

Elshehawey, E. F.; Elbarbary, Elsayed M. E.; Afifi, N. A. S.; Elshahed, Mostafa

doi:10.1016/s0096-3003(00)00094-1

Cited by 10 publications

(9 citation statements)

References 3 publications

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“…Fractional calculus (FC) has attracted the attention of several researchers [4,24,25], being applied in various scientific fields such as engineering, computational mathematics, fluid mechanics, among others [26][27][28][29]. The Grünwald-Letnikov definition based on the concept of fractional differential with fractional coefficient α ∈ C of a general signal x(t) is given by:…”

Section: Fractional-order Darwinian Particle Swarm Optimizationmentioning

confidence: 99%

Introducing the fractional-order Darwinian PSO

Couceiro

Rocha

Ferreira

et al. 2012

SIViP

138

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One of the most well-known bio-inspired algorithms used in optimization problems is the particle swarm optimization (PSO), which basically consists on a machinelearning technique loosely inspired by birds flocking in search of food. More specifically, it consists of a number of particles that collectively move on the search space in search of the global optimum. The Darwinian particle swarm optimization (DPSO) is an evolutionary algorithm that extends the PSO using natural selection, or survival of the fittest, to enhance the ability to escape from local optima. This paper firstly presents a survey on PSO algorithms mainly focusing on the DPSO. Afterward, a method for controlling the convergence rate of the DPSO using fractional calculus (FC) concepts is proposed. The fractional-order optimization algorithm, denoted as FO-DPSO, is tested using several well-known functions, and the relationship between the fractional-order velocity and the convergence of the algorithm is observed. Moreover, experimental results show that the FO-DPSO significantly outperforms the previously presented FO-PSO.

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Section: Fractional-order Darwinian Particle Swarm Optimizationmentioning

confidence: 99%

Introducing the fractional-order Darwinian PSO

Couceiro

Rocha

Ferreira

et al. 2012

SIViP

138

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“…. , N -1, equipped with initial conditions (see [3][4][5][6][7] and the references therein). For example, Elshehawey et al [5] considered the endolymph equation which can be used to describe the response of the semicircular canals to the angular acceleration.…”

Section: Introductionmentioning

confidence: 99%

The Green’s function of a class of two-term fractional differential equation boundary value problem and its applications

Wang

2020

Adv Differ Equ

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In this paper, we consider a Riemann-Liouville type two-term fractional differential equation boundary value problem. Some positive properties of the Green's function are deduced by using techniques of analysis. As application, we obtain the existence and multiplicity of positive solutions for a fractional boundary value problem under conditions that the nonlinearity f (t, x) may change sign and may be singular at t = 0, 1 and x = 0, and we also obtain the uniqueness results of positive solution for a singular problem by means of the monotone iterative technique.

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“…Multi-term fractional differential equations appear in the mathematical models of many real world problems. For example, multi-term fractional differential equations have been used to model various types of visco-elastic damping ( [20][21][22]). In [20], the authors introduced the Bagley-Torvik equation:…”

Section: Introductionmentioning

confidence: 99%