Symmetric Erdelyi-Kober Operators and their Applications to Generalized Weber-Orr Transforms
Abstract: In this paper, we establish formal integral transforms that generalize the classical Weber-Orr transform and its inverse by utilizing symmetric generalized Erdelyi-Kober fractional integral operators. Building upon asymmetric frameworks, we introduce modifications of the arbitrary order (μ,?) transform and systematically investigate two distinct parametric operational regimes: μ=?-α and μ=?+α for α>0. Through a series of technical lemmas and core inversion theorems, we derive exact solutions for unknown function mappings. Special cases, including reductions to the classical Weber-Orr transforms and formulations under zero-parameter kernels (k=0), are evaluated to demonstrate the consistency of this overarching symmetric operator framework.
Keywords: Weber-Orr transform, Erdelyi-Kober fractional integrals, Integral transforms, Inversion theorem, Symmetric operator framework
How to Cite?: Dr. Haresh Gambhir Chaudhari, "Symmetric Erdelyi-Kober Operators and their Applications to Generalized Weber-Orr Transforms", Volume 15 Issue 7, July 2026, International Journal of Science and Research (IJSR), Pages: 25-28, https://www.ijsr.net/getabstract.php?paperid=SR26627120412, DOI: https://dx.doi.org/10.21275/SR26627120412