Boundary Value Problem for Nonlinear Fractional Differential Equations of Variable Order Via Kuratowski Mnc Technique
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Date
2021
Journal Title
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Volume Title
Publisher
Springer
Open Access Color
GOLD
Green Open Access
Yes
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No
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Top 10%
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Abstract
In the present research study, for a given multiterm boundary value problem (BVP) involving the Riemann-Liouville fractional differential equation of variable order, the existence properties are analyzed. To achieve this aim, we firstly investigate some specifications of this kind of variable-order operators, and then we derive the required criteria to confirm the existence of solution and study the stability of the obtained solution in the sense of Ulam-Hyers-Rassias (UHR). All results in this study are established with the help of the Darbo's fixed point theorem (DFPT) combined with Kuratowski measure of noncompactness (KMNC). We construct an example to illustrate the validity of our observed results.
Description
Ali, Hakem/0000-0001-6145-4514; Mohammed Said, Souid/0000-0002-4342-5231; Inc, Mustafa/0000-0003-4996-8373
Keywords
Fractional Differential Equations Of Variable Order, Boundary Value Problem, Darbo'S Fixed Point Theorem, Measure Of Noncompactness, Ulam-Hyers-Rassias Stability, 26A33, 34K37, Ulam–Hyers–Rassias stability, Darbo’s fixed point theorem, Economics, Theory and Applications of Fractional Differential Equations, Mathematical analysis, Quantum mechanics, Database, Value (mathematics), Differential equation, Fractional differential equations of variable order, Numerical Integration Methods for Differential Equations, Machine learning, QA1-939, FOS: Mathematics, Measure of Noncompactness, Variable (mathematics), Fixed-point theorem, Stability (learning theory), Boundary value problem, Anomalous Diffusion Modeling and Analysis, Order (exchange), Measure of noncompactness, Numerical Analysis, Applied Mathematics, Physics, Statistics, Pure mathematics, Measure (data warehouse), Computer science, Darbo’s Fixed Point Theorem, Fractional Differential Equations of Variable Order, Ulam–Hyers–Rassias Stability, Boundary Value Problems, Boundary Value Problem, Modeling and Simulation, Physical Sciences, Nonlinear system, Mathematics, Ordinary differential equation, Finance, Applications of operator theory to differential and integral equations, fractional differential equations, Fractional ordinary differential equations, Darbo's fixed point theorem, Measures of noncompactness and condensing mappings, \(K\)-set contractions, etc., Fractional derivatives and integrals, boundary value problem, Ulam-Hyers-Rassias stability, measure of noncompactness, Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
Fields of Science
Citation
Benkerrouche, Amar...et al. (2021). "Boundary value problem for nonlinear fractional differential equations of variable order via Kuratowski MNC technique", Advances in Difference Equations, Vol. 2021, No. 1.
WoS Q
Q1
Scopus Q
OpenCitations Citation Count
20
Source
Advances in Difference Equations
Volume
2021
Issue
1
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CrossRef : 10
Scopus : 26
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