WoS İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653

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2010 - 20173

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Publisher: search.filters.publisher.Springer/plenum PublishersSubject: search.filters.subject.Fractional Calculus

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Now showing 1 - 3 of 3
  • Article
    Citation - WoS: 23
    Citation - Scopus: 23
    Conditional Optimization Problems: Fractional Order Case
    (Springer/plenum Publishers, 2013) Baleanu, Dumitru; Majd, Vahid Johari; Razminia, Abolhassan
    In this manuscript, we introduce a new formulation for the constrained optimization problems in which the objective function is considered in the fractional integral form. The constraints are applied in two separate cases, namely, fractional differential and fractional isoperimetric constraints. In both cases, by using the extended Euler-Lagrange equations and the Lagrange multiplier method, the necessary conditions are obtained. An example is given in order to illustrate the effectiveness of the reported results.
  • Article
    Citation - WoS: 80
    Citation - Scopus: 93
    A New Formulation of the Fractional Optimal Control Problems Involving Mittag-Leffler Nonsingular Kernel
    (Springer/plenum Publishers, 2017) Jajarmi, Amin; Hajipour, Mojtaba; Baleanu, Dumitru
    The aim of this paper is to propose a new formulation of the fractional optimal control problems involving Mittag-Leffler nonsingular kernel. By using the Lagrange multiplier within the calculus of variations and by applying the fractional integration by parts, the necessary optimality conditions are derived in terms of a nonlinear two-point fractional boundary value problem. Based on the convolution formula and generalized discrete Gronwall's inequality, the numerical scheme for solving this problem is developed and its convergence is proved. Numerical simulations and comparative results show that the suggested technique is efficient and provides satisfactory results.
  • Article
    Citation - WoS: 33
    Citation - Scopus: 35
    Is It Possible To Derive Newtonian Equations of Motion With Memory
    (Springer/plenum Publishers, 2010) Baleanu, D.; Nigmatullin, R. R.
    In this paper for a given example we proved that the Riemann-Liouville fractional integral term appears naturally and relates the external force with acceleration within the fractional Newtonian equation. The consideration of some self-similar process that leads to the fractional integral as well as some possible generalizations of the proposed model was discussed.