Neutral functional sequential differential equations with Caputo fractional derivative on time scales

In this paper, we establish the existence and uniqueness of a solution for a class of initial value problems for implicit fractional differential equations with Caputo fractional derivative. The arguments are based upon the Banach contraction principle, the nonlinear alternative of Leray–Schauder ty...

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Bibliographic Details
Published inFixed point theory and algorithms for sciences and engineering Vol. 2022; no. 1; pp. 1 - 16
Main Authors Lazreg, Jamal Eddine, Benkhettou, Nadia, Benchohra, Mouffak, Karapinar, Erdal
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.03.2022
Springer Nature B.V
SpringerOpen
Subjects
Algorithms
Analysis
Applications of Mathematics
Boundary value problems
Caputo’s fractional derivative
Control theory
Differential equations
Differential Geometry
Existence
Fixed point
Fixed points (mathematics)
Fractional integral
Initial value problem
Mathematical analysis
Mathematical and Computational Biology
Mathematics
Mathematics and Statistics
Sequential neutral functional differential equations
Topology
Caputo’s fractional derivative
Initial value problem
Fractional integral
26A33
Time scale
Existence
Sequential neutral functional differential equations
Fixed point
34A08
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Summary:In this paper, we establish the existence and uniqueness of a solution for a class of initial value problems for implicit fractional differential equations with Caputo fractional derivative. The arguments are based upon the Banach contraction principle, the nonlinear alternative of Leray–Schauder type and Krasnoselskii fixed point theorem. As applications, two examples are included to show the applicability of our results.
ISSN:2730-5422
2730-5422
DOI:10.1186/s13663-022-00716-9