Transmutations, Singular and Fractional Differential Equations with Applications to Mathematical Physics

Transmutations, Singular and Fractional Differential Equations with Applications to Mathematical Physics connects difficult problems with similar more simple ones. The book's strategy works for differential and integral equations and systems and for many theoretical and applied problems in mathematics, mathematical physics, probability and statistics, applied computer science and numerical methods. In addition to being exposed to recent advances, readers learn to use transmutation methods not only as practical tools, but also as vehicles that deliver theoretical insights.

Presents the universal transmutation method as the most powerful for solving many problems in mathematics, mathematical physics, probability and statistics, applied computer science and numerical methodsCombines mathematical rigor with an illuminating exposition full of historical notes and fascinating detailsEnables researchers, lecturers and students to find material under the single "roof"

Introduction Acknowledgement and thanks 1 Basic definitions and propositions 2 Basics of fractional calculus and fractional order differential equations 3 Essential of the transmutations 4 Weighted generalized functions generated by quadratic form 5 Buschman-Erdelyi integral and transmutation operators 6 Integral transforms compositions method for transmutations 7 Differential equations with Bessel operator 8 Applications of transmutations to the different problems 9 Fractional powers of Bessel operators 10 B-potentials theory 11 Fractional differential equations with singular coefficients Conclusion References