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Nonlocal Cauchy Problem via a Fractional Operator Involving Power Kernel in Banach Spaces

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Department of Mathematics-Computer, Faculty of Science, Necmettin Erbakan University, Konya 42090, Turkey
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Department of Mathematics, Faculty of Arts and Sciences, Çankaya University, Ankara 06530, Turkey
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Institute of Space Sciences, Magurele, P.O.Box MG-23, Ro 077125 Bucharest, Romania
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Author to whom correspondence should be addressed.
Fractal Fract 2019, 3(2), 27; https://doi.org/10.3390/fractalfract3020027
Received: 25 April 2019 / Revised: 9 May 2019 / Accepted: 13 May 2019 / Published: 16 May 2019
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. View Full-Text
Keywords: existence-uniqueness conditions; nonlocal Cauchy problem; Caputo–Fabrizio fractional derivative; Banach space existence-uniqueness conditions; nonlocal Cauchy problem; Caputo–Fabrizio fractional derivative; Banach space
MDPI and ACS Style

Keten, A.; Yavuz, M.; Baleanu, D. Nonlocal Cauchy Problem via a Fractional Operator Involving Power Kernel in Banach Spaces. Fractal Fract 2019, 3, 27.

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