Fit user defined probability distribution to data

I have some data and i need to find the parameters of the probability distribution that yield the best fit. This distribution was originaly presented in https://ieeexplore.ieee.org/abstract/document/4067122?casa_token=-fIf6vgyZbAAAAAA:Msq9X2ymWRCYIYBpgOAJ_CmU_N8u-9r0N8WbATqe5Hwt_BZxL_CGCZ9wBFsJZjCo6Jlqmbcx. The PDF equation that i need to use is given as , stands for the gamma function. I have read the documentation in https://www.mathworks.com/help/stats/work-with-custom-distributions-using-the-distribution-fitting-tool.html#d122e13506 , but i can not see an apparent way i could use this for my problem. My question are. Can i use the Distribution Fitter App for my case or any of the relevant functions? Is generally a way to implement this in matlab?

[Jeff Miller]

Since you have the PDF, if all else fails you can use fminsearch to find the parameter values that maximize the likelihood of your observed data.