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

By A. Keten, Mehmet Yavuz, Dumitru Băleanu. Fractal and Fractional, 2019

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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.

Subfields: Applied Mathematics, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/87f0b612785a9b3ae4bfc687136a37d2adf85961