Existence of Solution of Fractional Boundary Value Problem Including Mixed Derivative
Project no. 23365 · Status: Kapanmış · 2021
Summary
<p>This project mainly consists of five parts.</p><p>In the first chapter, firstly, information about how fractional analysis emerged and its history is given. Secondly, the importance and usage areas of fractional analysis in other disciplines are emphasized. Then, information about the studies on this subject is given. Finally, the problem we studied is introduced and its difference from other problems is emphasized.</p><p>In the second chapter, firstly, the definitions of fractional derivative and fractional integral are given. Then, some properties of fractional derivative and fractional integral are given. Finally, basic definitions and some theorems are given.</p><p>In the third chapter, firstly, the solution of the fractional nonlinear boundary value problem involving mixed derivatives is found. Secondly, the structure of the solution is examined.</p><p>In the fourth chapter, firstly, the necessary conditions for the existence of at least one solution are obtained by using the Banach contracting transformation principle and Kraskonelskii fixed point theorems. Also, examples are given for each theorem.</p><p>In the last part, firstly, a result of the information obtained in the light of this study is given. Secondly, it is emphasized that the project achieved its goal.</p>