Open AccessOn solutions of fractal fractional differential equations
Author(s) -
Abdon Atangana,
Ali Akgül
Publication year - 2021
Publication title -
discrete and continuous dynamical systems. series s
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.481
H-Index - 34
eISSN - 1937-1632
pISSN - 1937-1179
DOI - 10.3934/dcdss.2020421
Subject(s) - mathematics , fractal , mathematical analysis , nonlinear system , fractional calculus , fractal dimension , class (philosophy) , differential equation , ordinary differential equation , fractal derivative , dimension (graph theory) , pure mathematics , fractal analysis , physics , computer science , quantum mechanics , artificial intelligence
New 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.