The Uniqueness of Solutions of Fractional Differential Equations in University Mathematics Teaching Based on the Principle of Compression Mapping

Abstract

This paper uses the principle of compressed mapping to discuss the existence and uniqueness of the explicit finite difference method for the fractional diffusion equation with time delay. The Laplace transform method obtains the necessary expression form of the solution. At the same time, the existence theorem and the existence and uniqueness theorem of the solution to the boundary value problem is established. Finally, an example is given to verify the correctness of the conclusion. The experimental results show that the parallel algorithm proposed in this paper agrees with the exact solution.

Synchronization in Finite Time of Fractional-Order Complex-Valued Delayed Gene Regulatory Networks

“…As is well known, fruitful results based on the gene network of integer-order differential equations have been reported [17][18][19]. With the development of the theory of fractional-order calculus and fractional-order differential equations [20][21][22][23], various applications of gene regulatory networks that employ fractional-order calculus, such as the fields of medical science, control, and biotechnology, have shown distinct advantages due to the merits of memory and heredity properties, see [24][25][26] and the references therein. In [24], the results indicated that the most significant benefit of using gene regulatory networks with fractional orders for their memorability and hereditary properties is the enhancement in the dexterity and accuracy of models.…”