Existence Results of Solutions for Nonlinear Hadamard Fractional Boundary Value Problems
Project no. 22866 · Status: Kapanmış · 2021
Summary
<p>In recent years, fractional differential equations and fractional boundary value problems have begun to be studied, with the emphasis that it is more appropriate to use models with fractional order derivatives instead of integer order derivatives in real life problems. In addition, the fractional calculus technique, which took its place in the scientific world with the discovery of wide application areas such as physics, biology, control theory, heat transfer, analytical and numerical methods, and economics, has enabled and provides many studies. Considering these, in this research, it is aimed to develop and generalize the existing problems in the literature by considering the Hadamard fractional boundary value problems. Schauder fixed point theorem, fixed point theorems on the cone, monotonous iterative method are some of the basic methods to be applied to the studies to be obtained within the scope of the project. Because of its non-local nature, fractional differential theory is a very good tool for describing the heritable properties of various processes. This is an important advantage for fractional derivatives when compared to derivatives of integer order. Therefore, in this project, fractional differential equation has been studied.</p><p>At the same time, Hadamard fractional differential systems will be discussed throughout the research. Recently, Hadamard fractional differential systems with non-local boundary conditions over a finite or infinite interval have become an important research topic. Nonlinear Hadamard fractional differential equations and systems of equations over the infinite interval are a new topic and have been little researched by scientists. The boundary conditions discussed in the project have not yet been studied with the Hadamard fractional derivative on the infinite interval. For this reason, this subject was chosen for the project. Considering the application areas of fractional boundary value problems, it is thought that this research can reach many application areas.</p>