Unique mild solution for caputo's fractional perturbed evolution equations with state-dependent delay
EVOLUTION EQUATIONS AND CONTROL THEORY(2024)
摘要
. This study examines if there are any mild solutions for the perturbed partial functional and neutral functional evolution equations with statedependent delay when the derivative utilizes Caputo's fractional derivative, as well as whether any such solutions are unique. The solution itself determines how long the equations take to solve. The work proves the existence and uniqueness of these solutions using semigroup theory and the Banach contraction theorem in Banach spaces.
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关键词
Perturbed evolution equations,neutral problems,Caputo's fractional derivative,existence of solution,uniqueness,state-dependent delay,nonlinear alternative,fixed point,semigroup theory
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