2014

DOI: 10.4236/ajcm.2014.44028

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On Generalized High Order Derivatives of Nonsmooth Functions

Samaneh Soradi Zeid¹,

Ali Vahidian Kamyad²

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Eralized Derivatives1

Test Problems1

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Cited by 3 publications

(2 citation statements)

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“…Here, at first, we brifly introduce a practical GD which is proposed by [24,25] and use the new GDs for nonsmooth calculus of variations.…”

Section: Eralized Derivativesmentioning

confidence: 99%

“…Hence, by applying Remark 2.1 and using the Fourier series, the corresponding GEL equation (5.3) will be as follows [25]:…”

Section: Test Problemsmentioning

confidence: 99%

See 1 more Smart Citation

Approximate Solutions of Nonsmooth Systems via Generalized Euler-Lagrange and Hamiltonian Equations

¹

,

²

,

³

2016

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Recently the traditional calculus of variations has been extended to be applicable for systems containing nonsmooth function. In this paper, we have investigated the generalized derivative of nonsmooth functions. The obtained results were applied to investigate the generalized Euler-Lagrange and Hamilton equations for constrained system. The approach was applied within an illustrative.

“…Here, at first, we brifly introduce a practical GD which is proposed by [24,25] and use the new GDs for nonsmooth calculus of variations.…”

Section: Eralized Derivativesmentioning

confidence: 99%

“…Hence, by applying Remark 2.1 and using the Fourier series, the corresponding GEL equation (5.3) will be as follows [25]:…”

Section: Test Problemsmentioning

confidence: 99%

Approximate Solutions of Nonsmooth Systems via Generalized Euler-Lagrange and Hamiltonian Equations

¹

,

²

,

³

2016

View full text Add to dashboard Cite

Recently the traditional calculus of variations has been extended to be applicable for systems containing nonsmooth function. In this paper, we have investigated the generalized derivative of nonsmooth functions. The obtained results were applied to investigate the generalized Euler-Lagrange and Hamilton equations for constrained system. The approach was applied within an illustrative.

King algorithm: A novel optimization approach based on variable-order fractional calculus with application in chaotic financial systems

¹

,

²

,

³

et al. 2020

Chaos, Solitons & Fractals

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No abstract

Approximate Solutions for a Class of Fractional-Order Model of HIV Infection via Linear Programming Problem

Zeid¹,

2016

Self Cite

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In this paper, we provide a new approach to solve approximately a system of fractional differential equations (FDEs). We extend this approach for approximately solving a fractional-order differential equation model of HIV infection of CD4 + T cells with therapy effect. The fractional derivative in our approach is in the sense of Riemann-Liouville. To solve the problem, we reduce the system of FDE to a discrete optimization problem. By obtaining the optimal solutions of new problem by minimization the total errors, we obtain the approximate solution of the original problem. The numerical solutions obtained from the proposed approach indicate that our approximation is easy to implement and accurate when it is applied to a systems of FDEs.

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