Innovative approaches to initial and terminal value problems of fractional differential equations with two different derivative orders

This research investigates the properties of fractional differential equations characterized by variable orders, focusing on their existence, uniqueness, and Ulam-Hyers stability. By transforming the problem into an integral equation format, we established essential conditions and utilized well-know...

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Published in:Fixed point theory and algorithms for sciences and engineering Vol. 2025; no. 1; pp. 32 - 22
Main Authors: Refice, Ahmed, Bensaid, M’hamed, Souid, Mohammed Said, Boulaaras, Salah, Amara, Abdelkader, Radwan, Taha
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 06.11.2025
Springer Nature B.V
SpringerOpen
Subjects:
Analysis
Applications of Mathematics
Banach spaces
Boundary value problem
Boundary value problems
Calculus
Derivatives and integrals of variable order
Differential equations
Differential Geometry
Fixed point theorem
Fixed points (mathematics)
Fractional calculus
Fractional derivatives
Integral equations
Mathematical and Computational Biology
Mathematics
Mathematics and Statistics
Partial differential equations
Piecewise function
Stability
Topology
Ulam-Hyers stability
Uniqueness
Ulam-Hyers stability
Fixed point theorem
Boundary value problem
Derivatives and integrals of variable order
Piecewise function
26A33
34K37
Fractional derivatives
34A08
ISSN:2730-5422, 2730-5422
Online Access:Get full text
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Summary:This research investigates the properties of fractional differential equations characterized by variable orders, focusing on their existence, uniqueness, and Ulam-Hyers stability. By transforming the problem into an integral equation format, we established essential conditions and utilized well-known fixed-point theorems to derive our results. The application of these mathematical strategies enables us to confirm the existence, uniqueness, and stability of solutions for the equations under consideration. Additionally, to highlight the practical implications of our findings, we present a specific example that effectively illustrates the core outcomes of this study.
Bibliography:ObjectType-Article-1
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ISSN:2730-5422
2730-5422
DOI:10.1186/s13663-025-00812-6