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On solutions of fractal fractional differential equations. (English) Zbl 1481.34009

Summary: 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.

MSC:

34A08 Fractional ordinary differential equations
34A05 Explicit solutions, first integrals of ordinary differential equations
26A33 Fractional derivatives and integrals
33E12 Mittag-Leffler functions and generalizations
44A10 Laplace transform
65L05 Numerical methods for initial value problems involving ordinary differential equations
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