Transmutation Method for Solving Hyper-bessel Differential Equations Based on the Poisson-dimovski Transformation
نویسندگان
چکیده
Virginia Kiryakova Dedicated to the 75th anniversary of Professor Gary Roach Abstract A generalization of the Poisson-type integral transformation proposed by Dimovski is applied to hyper-Bessel differential equations of arbitrary order, as a transmutation operator. By this method, their solutions are written in an explicit form, by evaluating operators of the generalized fractional calculus of generalized trigonometric functions. A differential analogue of the Poisson-Dimovski transformation is also proposed and its applications to ”spherical” hyper-Bessel equations from Kamke’s book are illustrated. Mathematics Subject Classification: 26A33, 34A25, 34L40, 33C60, 33C20
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