2017/07/15 by Elina Shishkina, Shishkina, Elina L., С. М. Ситник +1 · 1 citation
Mathematics · #26A33 #44A15 #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #FOS: Mathematics #Fractional Differential Equations Solutions #Mathematical functions and polynomials
paper · pdf · doi:10.48550/arxiv.1707.04733
openalex publication_date 2017/07/15 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
In the paper we find solution representations in the compact integral form to\nthe Cauchy problem for a general form of the Euler--Poisson--Darboux equation\nwith Bessel operators via generalized translation and spherical mean operators\nfor all values of the parameter k, including also not studying before\nexceptional odd negative values. We use a Hankel transform method to prove\nresults in a unified way. Under additional conditions we prove that a\ndistributional solution is a classical one too. A transmutation property for\nconnected generalized spherical mean is proved and importance of applying\ntransmutation methods for differential equations with Bessel operators is\nemphasized. The paper also contains a short historical introduction on\ndifferential equations with Bessel operators and a rather detailed reference\nlist of monographs and papers on mathematical theory and applications of this\nclass of differential equations.\n