Qualitative analysis of an abstract neutral integro-differential equation with state-dependent argument

Bakhtawar Pervaiz ^[1] ; Akbar Zada ^[1] ; Afef Kallekh ^[1] ; Sana Ben Moussa ^[1] ; Ioan-Lucian Popa ^[2]
1. [1] University of Peshawar
  
  University of Peshawar
  
  Pakistán
2. [2] University of Alba Iulia, Transilvania University of Brasov
Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 24, Nº 6, 2025
Idioma: inglés
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Resumen
- This study focuses on the existence and uniqueness of mild solution for a new class of an abstract neutral integro-differential equation (IDEq) with state-dependent argument (SDA). The concepts of analytic semigroup of bounded linear operators (BLOs) and contraction mapping theorem play a major role in establishing our main results. On the basis of our obtained results we deduce several corollaries. Notably, in this article both Lipschitz and non-Lipschitz solutions of abstract neutral IDEq with SDA are investigated. An example of partial differential equation (DEq) with SDA, is presented at the end.