Reproducing Kernel Method for Fractional Derivative with Non-local and Non-singular Kernel

  • Ali AkgülEmail author
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 194)


Atangana and Baleanu introduced a derivative with fractional order to answer some outstanding questions that were posed by many investigators within the field of fractional calculus. Their derivative has a non-singular and nonlocal kernel. Therefore, we apply the reproducing kernel method to fractional differential equations with non-local and non-singular kernel. In this work, a new method has been developed for the newly established fractional differentiation. Examples are given to illustrate the numerical effectiveness of the reproducing kernel method when properly applied in the reproducing kernel space. The comparison of approximate and exact solutions leaves no doubt believing that the reproducing kernel method is very efficient and converges toward exact solution very rapidly.


Fractional calculus Atangana–Baleanu fractional derivative Reproducing kernel method 


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Authors and Affiliations

  1. 1.Siirt University Art and Science Faculty Department of MathematicsSiirtTurkey

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