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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Vydané v:Fixed point theory and algorithms for sciences and engineering Ročník 2025; číslo 1; s. 32 - 22
Hlavní autori: Refice, Ahmed, Bensaid, M’hamed, Souid, Mohammed Said, Boulaaras, Salah, Amara, Abdelkader, Radwan, Taha
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Cham Springer International Publishing 06.11.2025
Springer Nature B.V
SpringerOpen
Predmet:
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
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Abstract 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.
AbstractList 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.
Abstract 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.
ArticleNumber 32
Author Souid, Mohammed Said
Bensaid, M’hamed
Amara, Abdelkader
Radwan, Taha
Refice, Ahmed
Boulaaras, Salah
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  organization: Department of Management Information Systems, College of Business and Economics, Qassim University
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Keywords Ulam-Hyers stability
Fixed point theorem
Boundary value problem
Derivatives and integrals of variable order
Piecewise function
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Snippet This research investigates the properties of fractional differential equations characterized by variable orders, focusing on their existence, uniqueness, and...
Abstract This research investigates the properties of fractional differential equations characterized by variable orders, focusing on their existence,...
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StartPage 32
SubjectTerms 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
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Title Innovative approaches to initial and terminal value problems of fractional differential equations with two different derivative orders
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