Hi
I attach my integral. Would you please find the attachment file. I explain everything at attachment file. The integral contains Mittag-Leffler function. The integral is definite. How can I calculate this integral?
Thanks
Hi, due to its complexity I think that only a numerical method (quadrature formula) is useful to compute this integral for a fixed value of t.
Dear Jamaleddin Mostafavi,
Did you try to write the M-L function in its form of infinite sum, and change order of integration/summation?
For a software computation, see http://www.mathworks.com/matlabcentral/fileexchange/8738-mittag-leffler-function
Dear sir,
You can integrate the series. I mean, an integral of a sum (in this case, the M-L function is the sum), is equal to the sum of the integrals. As each term of the sum is a polynomial function, more or less x to a certain power, each integral in this sum of integrals can be calculated.
The result of this is a new series, which, very likely, is not a function any more defined in literature. What the meaning then is, I dont know. If you want to skip this, and go straight to numerical methods, that's your choice.
Best Regards,
Henri.
Hi
Regarding to your question, I no have deep knowledge about M-L function but as I saw that the integral with respect to ( tau) , but the M-L function formula as written in your text depends on ( z complex variable ), also the rest of symbols are coefficients which means the integral will be only to the term contains (tau) ...try
But if M-L function of (tau) instead of z , in this case see link below, would be help
https://advancesindifferenceequations.springeropen.com/articles/10.1186/1687-1847-2012-181
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