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

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. Mor...

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Bibliographic Details
Published inQualitative theory of dynamical systems Vol. 23; no. 3
Main Authors Ma, Yanli, Maryam, Maryam, Riaz, Usman, Popa, Ioan-Lucian, Ragoub, Lakhdar, Zada, Akbar
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.07.2024
Springer Nature B.V
Subjects
Boundary conditions
Difference and Functional Equations
Differential equations
Dynamical Systems and Ergodic Theory
Fixed points (mathematics)
Fractional calculus
Mathematical analysis
Mathematics
Mathematics and Statistics
Stability
Hadamard fractional derivative
93Dxx
34B15
Coupled system
26A33
Caputo fractional derivative
Hyers–Ulam stability
34A08
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Summary: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 jerk-type 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.
ISSN:1575-5460
1662-3592
DOI:10.1007/s12346-024-00971-8