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In the paper we study applications of integral transforms composition method(ITCM) for obtaining transmutations via integral transforms. It is possible toderive wide range of transmutation operators by this method. Classical integraltransforms are involved in the integral transforms composition method (ITCM) asbasic blocks, among them are Fourier, sine and cosine-Fourier, Hankel, Mellin,Laplace and some generalized transforms. The ITCM and transmutations obtainingby it are applied to deriving connection formulas for solutions of singulardifferential equations and more simple non-singular ones. We considerwell-known classes of singular differential equations with Bessel operators,such as classical and generalized Euler-Poisson-Darboux equation and thegeneralized radiation problem of A.Weinstein. Methods of this paper are appliedto more general linear partial differential equations with Bessel operators,such as multivariate Bessel-type equations, GASPT (Generalized AxiallySymmetric Potential Theory) equations of A.Weinstein, Bessel-type generalizedwave equations with variable coefficients,ultra B-hyperbolic equations andothers. So with many results and examples the main conclusion of this paper isillustrated: the integral transforms composition method (ITCM) of constructingtransmutations is very important and effective tool also for obtainingconnection formulas and explicit representations of solutions to a wide classof singular differential equations, including ones with Bessel operators.

Applications of integral transforms composition method (ITCM) to wave-type singular differential equations and index shift transmutations