TURK 2025

Modern artificial intelligence and neural network technologies are increasingly being used in the educational process, including in teaching physics. Neural network technologies allow you to personalize the learning process, adapting the material to the level of knowledge of each student, as well as automate knowledge verification and analyze typical errors. They are widely used in the...

In this study, we investigate the traveling wave solutions of the Fokas equation, a notable member of the nonlinear partial differential equation family, using the Auxiliary Equation Method. By employing an appropriate wave transformation, the equation is reduced to an ordinary differential equation, facilitating the derivation of exact solutions. Through the systematic application of the...

In this paper, we present a cancer model to study the complex interplay among stem cells, effectors cells, and tumor cells in the presence and absence of chemotherapy. We employed the novel fractal-fractional operator with a generalized Mittag-Leffler kernel to capture the non-local nature of cancer dynamics. The existence and uniqueness criteria of the fractal-fractional cancer model are...

In this paper, a regularized asymptotics of the solution of a singularly perturbed Cauchy problem for a telegraph equation is constructed and finded numerical solution. Singularly perturbed telegraph equations, in our formulation, have not been paid attention to by researchers. This is due to the appearance of oscillating terms in the asymptotics.
We tried to find the asymptotic solution of...

Quantum computing stands poised to revolutionize multiple sectors, with finance, economics, and sustainability at the forefront of potential beneficiaries. This presentation explores the transformative applications of quantum algorithms in these fields. In finance, we discuss quantum-enhanced portfolio optimization, risk analysis, and fraud detection. For economics, we examine quantum...

In this study, we investigate numerical solutions of the variable-order fractional mobile–immobile advection–dispersion model in the Caputo sense using the collocation finite element method. The fractional-order time derivative and the classical-order space derivative are discretized using the \L1 algorithm and the Crank–Nicolson approach, respectively. An approximate solution is then...

Today, excessive consumption and environmental pollution are among the most important threats to the lives of future generations. Sustainable development aims to leave a livable world for future generations by preventing the unconscious consumption of resources. Therefore, sustainable development is of vital importance for the future of humanity. It addresses economic, social and environmental...

This study addresses the solution of a first-order partial differential equation containing a small parameter that leads to boundary layer behavior, rendering classical solution methods ineffective. To tackle this, we employ asymptotic expansion techniques enhanced by boundary layer corrections. The problem involves an initial-boundary value formulation where the differential operator contains...

This study employs the modified Extended Direct Algebraic Method (m-EDAM) to generate and assess propagating solutions for fractional partial differential equations (FPDE) via the first integral approach, which includes Caputo’s fractional derivatives. The increasing population sizes, reaction-diffusion processes, and mathematical biology are three areas of research in which FPDE is crucial...

In controlling many real processes, the implementation of frequent changes in the values of control actions is either associated with great difficulties in implementation or is completely impossible. Therefore, from a practical point of view, there is a need to study optimal control problems on given classes, for example, on classes of piecewise constant, piecewise linear and other control...