Fractional Euler Method; An Effective Tool for Solving Fractional Differential Equations

Ahmed, Hoda F.

doi:10.21608/joems.2018.9460

Cited by 19 publications

(12 citation statements)

References 17 publications

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“…Some examples illustrating numerical comparisons between the Euler algorithm and the classical algorithm are presented in Ref. 41 to find the solution to a given dynamical system.…”

Section: Mathematical Modelsmentioning

confidence: 99%

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PIC micro-controller based synchronization of two fractional order jerk systems

Tagne

Bodo

Eyebe

et al. 2022

Sci Rep

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The paper studies a 3D Chaotic Jerk oscillator with fractional derivatives. An approach is proposed to implement it on a PIC16F877A microcontroller in order to reduce the requirements for multiple analogue electronic components such as resistors, capacitors, coils, multipliers, operational amplifiers, which are very bulky and consume a lot of power. The behaviours of the underlying system are analysed analytically, numerically and experimentally. It comes from this analysis that the fractional model exhibits chaotic dynamics when for parameters for which the equivalent integer derivative system exhibits limit-cycles. The synchronization under two closed initial conditions is also studied, highlighting one of the most common applications of the chaos concept.

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“…Some examples illustrating numerical comparisons between the Euler algorithm and the classical algorithm are presented in Ref. 41 to find the solution to a given dynamical system.…”

Section: Mathematical Modelsmentioning

confidence: 99%

“… To solve it numerically, one use the Euler algorithm. In fact, the Euler algorithm has only one step, and it is easy to implement because it requires fewer mathematical operations 41 . The Euler algorithm is described for Eq.…”

Section: Introductionmentioning

confidence: 99%

PIC micro-controller based synchronization of two fractional order jerk systems

Tagne

Bodo

Eyebe

et al. 2022

Sci Rep

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“…2: Step 2. For n = 0, 1, calculate the approximation solution, y 1 , y 2 using Fractional Euler method [27]:…”

Section: Algorithmmentioning

confidence: 99%

Numerical Solutions of Fractional Differential Equations by Using Fractional Explicit Adams Method

et al. 2020

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Differential equations of fractional order are believed to be more challenging to compute compared to the integer-order differential equations due to its arbitrary properties. This study proposes a multistep method to solve fractional differential equations. The method is derived based on the concept of a third-order Adam–Bashforth numerical scheme by implementing Lagrange interpolation for fractional case, where the fractional derivatives are defined in the Caputo sense. Furthermore, the study includes a discussion on stability and convergence analysis of the method. Several numerical examples are also provided in order to validate the reliability and efficiency of the proposed method. The examples in this study cover solving linear and nonlinear fractional differential equations for the case of both single order as α∈(0,1) and higher order, α∈1,2, where α denotes the order of fractional derivatives of Dαy(t). The comparison in terms of accuracy between the proposed method and other existing methods demonstrate that the proposed method gives competitive performance as the existing methods.

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“…The investigation of biological model of infection disease under fractional derivatives is an interesting study as compared to classical order derivative. Because fractional calculus provides dynamical interpretations of real world phenomenon with more degree of freedom (see few as [50] , [51] , [52] , [53] ).…”

Section: Introductionmentioning

confidence: 99%