Qualitative Investigation of Nonlinear Fractional Coupled Pantograph Impulsive Differential Equations

• Kamal Shah ^[4] ; Israr Ahmad ; Juan J. Nieto ^[1] ; Ghaus Ur Rahman ^[2] ; Thabet Abdeljawad ^[3]
  1. [1] Universidade de Santiago de Compostela

     Universidade de Santiago de Compostela

     Santiago de Compostela, España

     
  2. [2] University of Swat

     University of Swat

     Pakistán

     
  3. [3] China Medical University

     China Medical University

     Taiwán

     
  4. [4] Prince Sultan University & University of Malakand

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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

  • In this manuscript a qualitative analysis to a nonlinear coupled system of pantograph impulsive fractional differential equations (PIFDEs) is established. By the use of Banach and Krasnoselskii’s fixed-point theorems some adequate conditions for the existence and uniqueness of solution to the considered problem are developed. The advantage of using Krasnoselskii’s fixed-point theorem is that it uses slight relax compact conditions as compared to other fixed point results. Furthermore, the manuscript is enriched by adding some results about Ulam–Hyers type stability. Finally, with the help of pertinent examples, the obtained theoretical results are justified.