Akışkanlar dinamiğinde oskolkov denkleminin tam çözümler

Traveling wave solutions of the Oskolkov equation, which is a model describing the dynamics of an incompressible visco-elastic Kelvin-Voigt fluid, are investigated in this study. Complex trigonometric and complex hyperbolic solutions of Oskolkov equation are obtained using the sub equation method. In these obtained solutions, graphs are presented by assigning special values to the parameters. The presented graphics are drawn with a computer package program. Implemented method is powerful and an effective method to achieve the exact solutions of nonlinear partial differential equations (NPDEs).Bu çalışmada, sıkıştırılamaz bir visko-elastik Kelvin-Voigt akışkanının dinamiklerini tanımlayan bir model olan Oskolkov denkleminin gezici dalga çözümleri araştırıldı. Alt denklem yöntemini kullanarak Oskolkov denkleminin karmaşık trigonometrik ve karmaşık hiperbolik çözümleri elde edildi. Bu elde edilen çözümlerde parametrelere özel değerler atanarak grafikler sunuldu. Sunulan grafikler bir bilgisayar paket programı ile çizildi. Uygulanan yöntem, lineer olmayan kısmi diferansiyel denklemlerin tam çözümlerini üretmek için güçlü ve etkili bir yöntemdir

Exploring Advanced Analysis Technique for Shallow Water Flow Models with Diverse Applications

The present article focuses on the analytical approach using fractional orders and its application in the dynamics of physical processes. Fractional order models align better with experimental data compared to non-fractional ones. This study primarily focuses on employing the new approximate analytical method to solve shallow water models with fractional orders. Numerical examples within the Caputo fractional derivative showcase the method’s application. Results for both integer and fractional orders are graphically depicted, demonstrating the fractional solutions’ closeness to actual data. Analysis of 3D and 2D fractional order graphs reveals convergence toward integer order graphs as fractional derivatives approach non-fractional ones. This method shows promise for direct application in solving targeted problems and can be easily adapted for other fractional nature problems