Theory and applications on a new generalized Laplace-type integral transform - ALBAYRAK, DURMUŞ (My University, 2022)
In this paper, several theorems and relations are examined by using a generalized Laplace-type integral transform. A generalization of the harmonic oscillator in a non-resisting and resisting medium problems, initial-boundary problems, and integral equations is solved via this integral transform. Furthermore, the well-known series entitled as Basel problem is obtained in a similar way. Moreover, we compare numerically classical and newly introduced by us integral transform.
Keywords: Matematik; Bilgisayar Bilimleri; Temel Bilimler; Mathematics; Computer Science; Natural Sciences; MATEMATİK, UYGULAMALI; Temel Bilimler (SCI); MATHEMATICS, APPLIED; MATHEMATICS; Natural Sciences (SCI); Sayısal analiz; Modelleme ve Simülasyon; Uygulamalı matematik; Analiz; Cebir ve Sayı Teorisi; Matematik (çeşitli); Genel Matematik; Hesaplamalı Teori ve Matematik; Fizik Bilimleri; Numerical Analysis; Modeling and Simulation; Applied Mathematics; Analysis; Algebra and Number Theory; Mathematics (miscellaneous); General Mathematics; Computational Theory and Mathematics; Physical Sciences; convolution; differential equations; integral equations; Laplace transform; partial differential equations; convolution; differential equations; integral equations; Laplace transform; partial differential equations