WoS İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653
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Article Citation - WoS: 47Citation - Scopus: 57Nonlocal Cauchy Problem Via a Fractional Operator Involving Power Kernel in Banach Spaces(Mdpi, 2019) Yavuz, Mehmet; Baleanu, Dumitru; Keten, AysegulWe 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.Article Citation - WoS: 51Citation - Scopus: 88Chaos in a Cancer Model Via Fractional Derivatives With Exponential Decay and Mittag-Leffler Law(Mdpi, 2017) Guadalupe Lopez-Lopez, Maria; Manuel Alvarado-Martinez, Victor; Baleanu, Dumitru; Khan, Hasib; Francisco Gomez-Aguilar, Jose; Alvarado-Martínez, Victor Manuel; Gómez-Aguilar, José Francisco; López-López, María GuadalupeIn this paper, a three-dimensional cancer model was considered using the Caputo-Fabrizio-Caputo and the new fractional derivative with Mittag-Leffler kernel in Liouville-Caputo sense. Special solutions using an iterative scheme via Laplace transform, Sumudu-Picard integration method and Adams-Moulton rule were obtained. We studied the uniqueness and existence of the solutions. Novel chaotic attractors with total order less than three are obtained.