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An alternative approach for solving Kummer’s differential equations | ||
| Journal of University of Anbar for Pure Science | ||
| Volume 20, Issue 2, August 2026, Pages 395-403 PDF (330.67 K) | ||
| Document Type: Research Paper | ||
| DOI: 10.37652/juaps.2025.165191.1692 | ||
| Authors | ||
| Ahmad Issa* ; Murat Duz | ||
| Department of Mathematics, Faculty of Science, Karabuk University, Karabuk, Turkiye | ||
| Abstract | ||
| Kummer’s equation has been used in many physical, engineering, and scientific applications, including the study of the Boltzmann energy distribution, the hydrogen atom through transformation of the radial equation into Kummer’s equation, electrical-circuit modeling, and the solution of Laplace’s equation in circular and cylindrical coordinates. This paper presents an alternative solution to Kummer’s differential equation based on the Dirac delta distribution using the Fourier transform method (FTM). The proposed solution does not depend on Kummer’s confluent hypergeometric function or Gordon’s function. In addition, the Frobenius method was employed to solve the differential equation obtained after applying the Fourier transform method. The validity and effectiveness of the proposed method are demonstrated. However, in certain cases, classical solutions may be insufficient to describe singular phenomena or may fail to exist within standard function spaces. This motivates the study of generalized solutions formulated within the framework of distribution theory. | ||
| Keywords | ||
| Fourier Transform Method; Inverse Fourier Transform; Kummer’s differential equation; Dirac delta distribution | ||
| References | ||
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