Baleanu, DumitruGolmankhaneh, Alireza Khalili2017-04-192025-09-182017-04-192025-09-182016Golmankhaneh, A.R., Baleanu, D. (2016). New derivatives on the fractal subset of real-line. Entropy, 18(2). http://dx.doi.org/10.3390/e180200011099-4300https://doi.org/10.3390/e18020001https://hdl.handle.net/20.500.12416/11178Khalili Golmankhaneh, Alireza/0000-0002-5008-0163In this manuscript we introduced the generalized fractional Riemann-Liouville and Caputo like derivative for functions defined on fractal sets. The Gamma, Mittag-Leffler and Beta functions were defined on the fractal sets. The non-local Laplace transformation is given and applied for solving linear and non-linear fractal equations. The advantage of using these new nonlocal derivatives on the fractals subset of real-line lies in the fact that they are better at modeling processes with memory effect.eninfo:eu-repo/semantics/openAccessMemory ProcessesGeneralized Mittag-Leffler FunctionGeneralized Gamma FunctionGeneralized Beta FunctionFractal CalculusTriadic Cantor SetNon-Local Laplace TransformationArticle10.3390/e180200012-s2.0-84960419770