Impulsive Integrodifferential Equations Involving Nonlocal Initial Conditions
Copyright policy )Impulsive Integrodifferential Equations Involving Nonlocal Initial Conditions
The authors study the existence and uniqueness of mild solutions for the Cauchy problem for impulsive Riemann-Liouville integro-differential equations involving non-local initial condition: \[ \begin{gathered} u'(t)- \int^t_0 {(t- s)^{\alpha-2}\over \Gamma(\alpha- 1)} Au(s)\,ds= F(t,u(t)),\quad 0\leq t\leq a,\;t\neq t_1,\\ u(0)= H(u),\\ u(t^+_i)= u(t^-_i)+ T_i(u(t^-_i))\quad (i= 1,2,\dots, n),\end{gathered} \] where \(1 t_n> a\), \(u(t^{+-}_i)\) stand for the right and left limits.
- Nanchang University China (People's Republic of)
- NANCHANG UNIVERSITY China (People's Republic of)
- Nanchang University China (People's Republic of)
Cauchy problem, Integro-ordinary differential equations, Algebra and Number Theory, Applied Mathematics, impulsive integro-differential equations, Riemann-Liouville integral, QA1-939, Ordinary differential equations with impulses, Mathematics, Analysis
Cauchy problem, Integro-ordinary differential equations, Algebra and Number Theory, Applied Mathematics, impulsive integro-differential equations, Riemann-Liouville integral, QA1-939, Ordinary differential equations with impulses, Mathematics, Analysis
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