Uniqueness of solution for higher-order nonlinear fractional differential equations with multi-point and integral boundary conditions

This study is devoted to the development of alternative conditions for existence and uniqueness of nonlinear fractional differential equations of higher-order with integral and multi-point boundary conditions. It uses a novel approach of employing a fixed point theorem based on contractive iterates...

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Published inRevista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas Vol. 115; no. 3
Main Authors Sevinik-Adıgüzel, Rezan, Aksoy, Ümit, Karapınar, Erdal, Erhan, İnci M.
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.07.2021
Springer Nature B.V
Subjects
Applications of Mathematics
Boundary conditions
Differential equations
Existence theorems
Fixed points (mathematics)
Integrals
Mathematical analysis
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Operators (mathematics)
Original Paper
Theoretical
Uniqueness theorems
46J10
47H10
Metric space
Fractional differential equations
Fixed point
54H25
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Summary:This study is devoted to the development of alternative conditions for existence and uniqueness of nonlinear fractional differential equations of higher-order with integral and multi-point boundary conditions. It uses a novel approach of employing a fixed point theorem based on contractive iterates of the integral operator for the corresponding fixed point problem. We start with developing an existence-uniqueness theorem for self-mappings with contractive iterate in a b-metric-like space. Then, we obtain the unique solvability of the problem under suitable conditions by utilizing an appropriate b-metric-like space.
ISSN:1578-7303
1579-1505
DOI:10.1007/s13398-021-01095-3