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TR-Dizin İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8652

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Browsing TR-Dizin İndeksli Yayınlar Koleksiyonu by Journal "An International Journal of Optimization and Control: Theories & Applications (IJOCTA)"

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    Article
    Citation - WoS: 4
    Citation - Scopus: 5
    An algebraic stability test for fractional order time delay systems
    (Ramazan Yaman, 2020) Ozyetkin, Munevver Mine; Baleanu, Dumitru; 56389; Matematik
    In this study, an algebraic stability test procedure is presented for fractionalorder time delay systems. This method is based on the principle of eliminatingtime delay. The stability test of fractional order systems cannot be examineddirectly using classical methods such as Routh-Hurwitz, because such systemsdo not have analytical solutions. When a system contains the square roots ofs, it is seen that there is a double value function of s. In this study, a stabilitytest procedure is applied to systems including ps and/or different fractionaldegrees such as s where 0 < α < 1, and αǫR. For this purpose, the integerorder equivalents of fractional order terms are first used and then the stabilitytest is applied to the system by eliminating time delay. Thanks to the proposedmethod , it is not necessary to use approximations instead of time delay termsuch as Pad´e. Thus, the stability test procedure does not require the solutionof higher order equations.
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    Article
    On solutions of variable-order fractional differential equations
    (2017) Akgül, Ali; Inc, Mustafa; Baleanu, Dumitru; 56389; Matematik
    Numerical calculation of the fractional integrals and derivatives is the code tosearch fractional calculus and solve fractional differential equations. The exactsolutions to fractional differential equations are compelling to get in real ap-plications, due to the nonlocality and complexity of the fractional differentialoperators, especially for variable-order fractional differential equations. There-fore, it is significant to enhance numerical methods for fractional differentialequations. In this work, we consider variable-order fractional differential equa-tions by reproducing kernel method. There has been much attention in theuse of reproducing kernels for the solutions to many problems in the recentyears. We give an example to demonstrate how efficiently our theory can beimplemented in practice.