Related to your query, a recomended textbook is here : https://link.springer.com/book/10.1007/BFb0067095

However,. you may also follow https://www.gcsu.edu/sites/files/page-assets/node-808/attachments/mctier.pdf

https://label2.tecnico.ulisboa.pt/vilela/Cursos/Frac_calcul.pdf

1) The Fractional Calculus Theory and Applications of Differentiation and Integration to Arbitrary Order by Keith B. Oldham, Jerome Spanier

2) Kilbas,_H.M._Srivastava,_J.J._Trujillo. Theory and Applications of Fractional Differential Equations. Elsevier, Amsterdam (2006)

3) Samko, S.G., Kilbas, A.A. and Marichev, O.I. Fractional Integrals and Derivative. Theory and Applications. Gordon & Breach Sci. Publishers, 1993

Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications

Ignor Podlubny and Kenneth V. Thimann (Eds.)

I recommended the following book:

Kindergarten of Fractional Calculus

This book presents a simplified deliberation of fractional calculus, which will appeal not only to beginners, but also to various applied science mathematicians and engineering researchers. The text develops the ideas behind this new field of mathematics, beginning at the most elementary level, before discussing its actual applications in different areas of science and engineering.

Which do you suggest the most useful of mathematical software program on mathematical modelling?

Dear Taylan Demir . See the following useful link: https://www.mdpi.com/books/pdfview/book/755

Kindly see also the following very useful link contains a lot of free pdf books : https://mechatronics.ucmerced.edu/fcbooks

Here is a good book on anomalous transport and fractional calculus:

Anomalous Transport: Foundations and Applications, Edited by Rainer Klages, Günter Radons, and Igor M. Sokolov, WILEY-VCH Verlag GmbH & Co. KGaA (2008)

This book is closely related to the application of fractional calculus to those complex trnsport problems.