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The Generic Nonlocal Fractal Calculus
  • Rawid Banchuin
Rawid Banchuin
Siam University

Corresponding Author:rawid.ban@siam.edu

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The generic nonlocal fractal calculus scheme have been formulated in this work. A unified derivative operator which employs an interpolated characteristic between the generic nonlocal derivative in Riemann–Liouville and Caputo senses has also been derived. For being generic, an arbitrary kernel function has been adopted. The condition on fractional order has been derived so that it is not related to the γ-dimension of the fractal set. The fractal Laplace transforms of our operators have been derived. A simple illustrative example and practical ones have been presented. Unlike the previous power law kernel-based nonlocal fractal calculus operators, ours are generic, consistent with the local fractal derivative and employ higher degree of freedom. The inverse relationships between our derivative and integral operators can be achieved. The results obtained from the examples are significantly different from such previous operator-based counterparts and significantly depended on the kernel function. The unified operator displays an interpolated characteristic as expected.