Abstract
In this paper, we investigate the implementations of newly introduced nonlocal differential operators as convolution of power law, exponential decay law, and the generalized Mittag-Leffler law with fractal derivative in fluid dynamics. The new operators are referred as fractal-fractional differential operators. The governing equations for the problem are constructed with the fractal-fractional differential operators. We present the stability analysis and the error analysis.
Highlights
Magnetohydrodynamics (MHD) deals with the study of the motion of electrically conducting fluids in the presence of the magnetic field
Farman et al [24] have analyzed the numerical solution of SEIR Epidemic model of measles with noninteger time fractional derivatives by using the Laplace Adomian decomposition method
Ghanbari and Atangana [26, 27] have given the new edge detecting techniques based on fractional derivatives with nonlocal and nonsingular kernels
Summary
Magnetohydrodynamics (MHD) deals with the study of the motion of electrically conducting fluids in the presence of the magnetic field. Ghanbari and Djilali [25] have taken mathematical analysis of a fractional-order predator-prey model with prey social behavior and infection developed in predator population. Ghanbari and Atangana [26, 27] have given the new edge detecting techniques based on fractional derivatives with nonlocal and nonsingular kernels. Another idea of differentiation has been proposed by Atanagna [28].
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