THE IMPORTANCE OF DIFFERENTIAL EQUATIONS WITH PARTICULAR DERIVATIVES IN MATHEMATICS

Differential equations with definite derivatives play a fundamental role in modern mathematics and its applications in science and engineering. This study studies the theoretical and practical significance of differential equations involving certain types of derivatives, such as partial, fractional, and higher-order derivatives. In general, differential equations with definite derivatives extend the classical theory and provide powerful tools for solving real-world problems, which demonstrates their important importance in both pure and applied mathematics.