Fractional and Multivariable Calculus by A.M. Mathai & H.J. Haubold

Author:A.M. Mathai & H.J. Haubold
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

Solution 3.2

This can be solved by a simple property of matrices. To this end, write one more equation that is an identity and write the system of equations:

(i)

Take

Then the equation in (ii) can be written as

But from the initial condition

From (iii)

Therefore, we need to compute only because is already known. For example, if , then we need to multiply A by itself 100 times, which is not an easy process. Hence, we will make use of some properties of eigenvalues. Let us compute the eigenvalues of A.

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