Browsing by Author "Yavuz, Mehmet"

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Citation Count: Bonyah, Ebenezer...et al. (2020). "A robust study on the listeriosis disease by adopting fractal-fractional operators", Alexandria Engineering Journal, Vol. 61, No. 3, pp. 2016-2028.
A robust study on the listeriosis disease by adopting fractal-fractional operators
(2020) Bonyah, Ebenezer; Yavuz, Mehmet; Baleanu, Dumitru; Kumar, Sunil; 56389
Listeriosis is one of the zoonotic diseases affecting most parts of the Sub-Saharan countries. The infection is often transmitted by eating and it can also pass by respiratory and direct contact. In this paper, a listeriosis mathematical model is formulated involving fractal-fractional orders in both Caputo and Atangana-Baleanu derivatives. Moreover, future behaviors of the disease are investigated by considering the fractal-fractional operators that are very effective in modeling the real-life phenomena by virtue of their memory effect. The basic properties and steady states are also obtained. The threshold parameter for determining the spread of the disease is computed. Numerical results are presented for each fractal-fractional-order operator. The results obtained in the paper show that the numerical schemes are effective for predicting and analyzing complex phenomena. (C) 2019 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University.
Citation Count: Keten, Aysegul; Yavuz, Mehmet; Baleanu, Dumitru, "Nonlocal Cauchy Problem via a Fractional Operator Involving Power Kernel in Banach Spaces", Fractal and Fractional, Vol. 3, No. 2, (June 2019)
Nonlocal Cauchy Problem via a Fractional Operator Involving Power Kernel in Banach Spaces
(MDPI, 2019) Keten, Ayşegül; Yavuz, Mehmet; Baleanu, Dumitru; 56389
We investigated existence and uniqueness conditions of solutions of a nonlinear differential equation containing the Caputo-Fabrizio operator in Banach spaces. The mentioned derivative has been proposed by using the exponential decay law and hence it removed the computational complexities arising from the singular kernel functions inherit in the conventional fractional derivatives. The method used in this study is based on the Banach contraction mapping principle. Moreover, we gave a numerical example which shows the applicability of the obtained results.