Dual Identities in Fractional Difference Calculus Within Riemann
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Date
2013
Authors
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Publisher
Springeropen
Open Access Color
GOLD
Green Open Access
Yes
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Abstract
We investigate two types of dual identities for Riemann fractional sums and differences. The first type relates nabla- and delta-type fractional sums and differences. The second type represented by the Q-operator relates left and right fractional sums and differences. These dual identities insist that in the definition of right fractional differences, we have to use both nabla and delta operators. The solution representation for a higher-order Riemann fractional difference equation is obtained as well.
Description
Abdeljawad, Thabet/0000-0002-8889-3768
ORCID
Keywords
Right (Left) Delta And Nabla Fractional Sums, Right (Left) Delta And Nabla Riemann, Q-Operator, Dual Identity, Economics, Dynamical Systems (math.DS), Operator (biology), Theory and Applications of Fractional Differential Equations, Mathematical analysis, Biochemistry, Quantum mechanics, Gene, Convergence Analysis of Iterative Methods for Nonlinear Equations, Differential equation, Nabla symbol, FOS: Mathematics, Mathematics - Dynamical Systems, Biology, Anomalous Diffusion Modeling and Analysis, Order (exchange), Numerical Analysis, Algebra and Number Theory, Omega, Ecology, Applied Mathematics, Dual (grammatical number), Physics, Fractional calculus, Pure mathematics, Partial differential equation, Fractional Derivatives, Chemistry, Literature, Modeling and Simulation, FOS: Biological sciences, Physical Sciences, Repressor, Transcription factor, 26A33, Type (biology), Analysis, Mathematics, Ordinary differential equation, Art, Finance, Riemann hypothesis, right (left) delta and nabla Riemann, Fractional derivatives and integrals, right (left) delta and nabla fractional sums, Riemann fractional difference equation, dual identity, \(Q\)-operator, Difference operators
Fields of Science
02 engineering and technology, 01 natural sciences, 0103 physical sciences, 0202 electrical engineering, electronic engineering, information engineering
Citation
Abdeljawad, T. (2013). Dual identities in fractional difference calculus within Riemann. Advance in Difference Equations, 36(36), 1-16. http://dx.doi.org/10.1186/1687-1847-2013-36
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Q1
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OpenCitations Citation Count
69
Source
Advances in Difference Equations
Volume
2013
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