Atangana, AbdonAkgul, Ali2024-12-242024-12-2420211937-16321937-1179https://doi.org/10.3934/dcdss.2020421https://hdl.handle.net/20.500.12604/8362New class of differential and integral operators with fractional order and fractal dimension have been introduced very recently and gave birth to new class of differential and integral equations. In this paper, we derive exact solution of some important ordinary differential equations where the differential operators are the fractal-fractional. We presented a new numerical scheme to obtain solution in the nonlinear case. We presented the numerical simulation for different values of fractional orders and fractal dimension.eninfo:eu-repo/semantics/openAccessFactal fractional derivativespower law kernelexponential decay kernelMittag-Leffler kernelLaplace transformArticle141034413457Q2WOS:000678575000007Q12-s2.0-8509868927910.3934/dcdss.2020421