Speaker
Description
We discuss existence results for solutions to some classes of nonlinear impulsive dynamic equations on time scales. By applying modern techniques in fixed point theory, specifically expansive mappings, $k$-set contractions, and cone methods, we derive criteria for the existence of at least one and multiple solutions. Our methodology removes the standard boundedness assumptions often required for nonlinear terms, thereby allowing for more general and flexible terms in the governing equations. Furthermore, we discuss the extension of these frameworks to fractional impulsive systems, emphasizing the integration of fixed point index theory with expansive operators. The theoretical findings are supported by illustrative examples that demonstrate their practical utility and relevance.
