Which kernel in fractional derivatives could be better for modeling and analysing the dynamic behavior of fractional models: Singular; Non-singular & local; Non-singular & nonlocal ?
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Dear Dr. Ashish Rayal
At this time, in most of the mathematical modelings, the researchers apply fractional operators with non-singular kernels such as Caputo-Fabrizio fractional derivatives and Atangana-Baleanu fractional derivatives. even, these new operators decrease the complexity of computations.
Some consider this science part of mathematical analysis and deals with the applications of integration and derivation in the case of optional ranks, and this field is concerned with generalizing the derivative to an association (function) for any derivative of an incorrect rank, for example: we usually deal with the first and second derivative. As for this field (fractional differentiation), it helps us to find the derivative number half or 0.3
Classic operators, the partial integral is introduced and then used to define Fractional derivative in a way that may be semi-complex. Whereas, in new types of fractional operators with an irrational core, the fractional derivative is introduced and then implemented to define the fraction Simplified integrations
By applying the system of difference equations, the stability conditions for the positive equilibrium point of the system are obtained. Its fractal form is determined using the regular form and the center manifold theorem. In addition, the effect of the nucleus in the fractal order Then check the dynamic behavior of the system. Numerical simulation is used Demonstrate the accuracy of the analytical results
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