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    Öğe
    Generalized Hukuhara diamond-alpha derivative of fuzzy valued functions on time scales
    (Ankara University Faculty of Sciences, 2025) Bayeg, Selami; Mert, Funda Raziye
    In the literature, the delta and nabla derivatives have been considered separately in the study of fuzzy number valued functions on time scales. In this paper, to unify these two derivatives for fuzzy number valued functions, we propose a new dynamic derivative called the diamond-alpha derivative, defined via the generalized Hukuhara difference. We establish several fundamental properties of the diamond-alpha derivative and investigate a particular class of fuzzy initial value problems on time scales with respect to this new derivative. Additionally, we provide numerical examples to illustrate our results.
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    ON THE OSCILLATION OF KERNEL FUNCTION DEPENDENT FRACTIONAL INTEGRODIFFERENTIAL EQUATIONS
    (Rocky Mt Math Consortium, 2022) Mert, Raziye; Bayeg, Selami; Abdeljawad, Thabet; Abdalla, Bahaaeldin
    We deal with the oscillation of a class of generalized fractional integrodifferential equations containing a forcing term. We establish sufficient conditions to obtain some oscillation criteria for the RiemannLiouville and Caputo cases. Moreover, we provide several examples to support our results.
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    Singularly perturbed fuzzy initial value problems
    (Pergamon-Elsevier Science Ltd, 2023) Dogan, Nurettin; Bayeg, Selami; Mert, Raziye; Akin, Oemer
    In this work, we have firstly introduced singularly perturbed fuzzy initial value problems (SPFIVPs) and then we have given an algorithm for the solutions of them by using the extension principle given by Zadeh. We have presented some results on the behaviour of the.alpha -cuts of the solutions. To show the robustness of the given algorithm, we have fuzzified some examples given in the literature and then we have applied the algorithm.
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    SOME OSCILLATION CRITERIA FOR NONLOCAL FRACTIONAL PROPORTIONAL INTEGRODIFFERENTIAL EQUATIONS
    (Rocky Mountain Mathematics Consortium, 2025) Mert, Raziye; Bayeg, Selami
    We investigate the oscillation of a class of generalized proportional fractional integrodifferential equations with forcing term. We present sufficient conditions to prove some oscillation criteria in both of the Riemann-Liouville and Caputo cases. Besides, we present some numerical examples for applicability of our results.