Results on nonlocal controllability for impulsive fractional functional integro-differential equations via degree theory

This manuscript mainly focuses on the nonlocal controllability analysis for the impulsive fractional functional integro-differential equation (IFrFIDE) in n-dimensional Euclidean space. To attain the solution representation of the given system, we use the Laplace transform technique and the Mittag-Leffler function. Initially, we obtained the existence and uniqueness of a solution by using the topological degree method, contraction mapping and Gronwall's inequality. Moreover, we also explore the nonlocal controllability results for our given problem. Furthermore, two numerical examples and a filter system are provided for our given dynamical system. It is helpful to demonstrate the efficacy of our findings.

Automated summary

This manuscript mainly focuses on the nonlocal controllability analysis for the impulsive fractional functional integro-differential equation (IFrFIDE) in n-dimensional Euclidean space. Solution representation of the given system is obtained using Laplace transform technique and the Mittag-Leffler function. Existence and uniqueness of solution are proved using topological degree method, contraction mapping, and Gronwall's inequality. Nonlocal controllability results for the given problem are explored. Numerical examples and a filter system are provided to demonstrate the efficacy of the findings.