One of the great advantages of the Caputo fractional derivative is that it allows traditional initial and boundary conditions to be included in the formulation of the problem. In addition, its derivative for a constant is zero.
It is better than others, At classical order all derivatives have same exact answer but in fractional order, Caputo is near to exact also it allows initial and boundary conditions.
Strong mathematical justifications are presented to show that the non-singular kernel variations have serious flaws that should prevent their adoption.
See: K. Diethelm, R. Garrappa, A. Giusti, and M. Stynes, “Why fractional derivatives with nonsingular kernels should not be used,” Fractional Calculus and Applied Analysis, vol. 23, no. 3, pp. 610–634, 2020
The fractional derivative of a constant is zero, and the fractional differential equation of the Caputo type has initial conditions that are of the classical derivative type. These are the two key benefits of this technique over R-L derivative.
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