Existence and Hyers–Ulam Stability of Jerk-Type Caputo and Hadamard Mixed Fractional Differential Equations

Yanli Ma ^[3] ; Maryam Maryam ^[1] ; Usman Riaz ^[2] ; Ioan-Lucian Popa ^[4] ; Lakhdar Ragoub ^[5] ; Akbar Zada ^[1]
1. [1] University of Peshawar
  
  University of Peshawar
  
  Pakistán
2. [2] Qurtuba University of Science and Information Technology
  
  Qurtuba University of Science and Information Technology
  
  Pakistán
3. [3] Anhui Xinhua University
4. [4] University of Alba Iulia & Transilvania University of Brasov
5. [5] University of Prince Mugrin
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Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº 3, 2024
Idioma: inglés
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Resumen
- This article is concerned with existence of mild solutions for jerk-type fractional differential equations in the sense of Hadamard and Caputo fractional derivatives with separated boundary conditions. For the uniqueness of mild solutions in both cases, Banach contraction principle are followed. Moreover, at least one mild solution of jerktype Caputo–Hadamard and Hadamard–Caputo fractional differential equations can be analyzed using Krasnoselskii’s and Leray–Schauder fixed point theorems. Hyers– Ulam stability and its generalized case for both type of mentioned jerk-type problems can be find out with the help of some conditions and definitions. For the illustration of main results, an example is provided.