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- Kitap BölümüYalnız künye2025Investigation of Fractional Order Genesio-Tesi System Using Laplace Transformation
Bekiryazici, Zafer; Sengul, Suleyman; Merdan, Mehmet
In this paper the fractional-order Genesio-Tesi chaotic system is investigated with Laplace transformation method. Genesio-Tesi system is a three-dimensional equation system with quadratic nonlinearity and is frequently used for exemplifying chaotic systems. In this study, Caputo fractional derivative is used to obtain the fractional system and Laplace transformation is applied in order to analyze the explicit solutions of the system.
- MakaleAçık Erişim2025Investigation of fractional order covid-19 model with q-homotopy analysis transform method
Merdan, Mehmet; Açikgöz, Pınar
The primary objective of this paper is to derive approximate analytic solutions for the time fractional-order Covid-19 model by employing the q-homotopy analysis transform method (q-HATM) and the Laplace transform homotopy perturbation method (LT-HPM). The covid 19 model is a system of five-dimensional nonlinear ordinary differential equations. Moreover, this method applies even to more complex partial differential equations originating from mathematical biology, demonstrating computational efficiency and wide application. In this study, Caputo fractional derivative is used to obtain the fractional system and Laplace transformation is applied to analyze the approximate solutions of the system. Graphical results are presented and discussed quantitatively to illustrate the approximate solution. Copyright 2021, Yıldız Technical University.
- MakaleYalnız künye2016Multiplicative Laplace transform and its applications
Yalcin, Numan; Celik, Ercan; Gokdogan, Ahmet
In this work, taking definitions and properties of Laplace transform in classical analysis as a basis, we give some basic definitions and properties of the multiplicative Laplace transform. In addition, solutions of some multiplicative differential equations are obtained by the help of this transform.