A Note on the Existence and Controllability Results for Fractional Integrodifferential Inclusions of Order r ∈ (1, 2] with Impulses

V. Vijayakumar ^[3] ; M. Mohan Raja ^[3] ; Anurag Shukla ^[4] ; Juan J. Nieto ^[1] ; Kottakkaran Sooppy Nisar ^[2]
1. [1] Universidade de Santiago de Compostela
  
  Universidade de Santiago de Compostela
  
  Santiago de Compostela, España
2. [2] Prince Sattam Bin Abdulaziz University
  
  Prince Sattam Bin Abdulaziz University
  
  Arabia Saudí
3. [3] Vellore Institute of Technology
4. [4] Rajkiya Engineering College
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Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 21, Nº 4, 2022
Idioma: inglés
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Resumen
- This paper investigates the issue of existence and approximate controllability results for impulsive fractional differential inclusions with delay of orderr ∈ (1, 2] in Banach space. To begin, we analyze existence results for impulsive fractional evolution inclusions with delay using fractional calculations, the r-order cosine family, multivalued maps, and Martelli’s fixed point theorem. The approximate controllability results for impulsive fractional evolution inclusions with delay were then derived using Gronwall’s inequality and the sequence method. Then, we investigate the Sobolev fractional integrodifferential inclusions with finite delay. Moreover, we develop the nonlocal conditions in a given system. Finally, an example is presented to illustrate the main results.