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Nabla Discrete fractional Calculus and Nabla Inequalities [PDF]
Mathematical and Computer Modelling, 2009 Here we define a Caputo like discrete nabla fractional difference and we produce discrete nabla fractional Taylor formulae for the first time. We estimate their remaiders.
Anastassiou, George A.
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Discrete-time Mittag–Leffler state estimation for fractional-order quaternion memristive neural networks [PDF]
Scientific ReportsThis article investigates the state estimation of fractional-order memristive systems with discrete-time terms. By considering discrete fractional calculus, we propose a novel and efficient criterion for ensuring the global Mittag–Leffler stability of ...
Qun Huang, Zhengwen Tu
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Nonlinear discrete fractional sum inequalities related to the theory of discrete fractional calculus with applications [PDF]
Advances in Difference Equations, 2021 By means of ς fractional sum operator, certain discrete fractional nonlinear inequalities are replicated in this text. Considering the methodology of discrete fractional calculus, we establish estimations of Gronwall type inequalities for unknown ...
Zareen A. Khan +3 more
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Hardy-type inequalities in fractional h-discrete calculus [PDF]
Journal of Inequalities and Applications, 2018 The first power weighted version of Hardy’s inequality can be rewritten as ∫0∞(xα−1∫0x1tαf(t)dt)pdx≤[pp−α−1]p∫0∞fp(x)dx,f≥0,p≥1 ...
Lars-Erik Persson +2 more
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Discrete fractional calculus with the nabla operator
Electronic Journal of Qualitative Theory of Differential Equations, 2009 Properties of discrete fractional calculus in the sense of a backward difference are introduced and developed. Exponential laws and a product rule are developed and relations to the forward fractional calculus are explored.
F. M. Atici, Paul Eloe
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Stability analysis of discrete delta fractional models under summation multipoint constraints for robust engineering systems [PDF]
Scientific ReportsWhen real-world systems like sensor networks or controllers face small disturbances, do their discrete fractional models stay reliable? We tackle this for a critical but unstudied problem: discrete delta fractional equations with summation multipoint ...
Pshtiwan Othman Mohammed +4 more
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On Sumudu Transform Method in Discrete Fractional Calculus [PDF]
Abstract and Applied Analysis, 2012 In this paper, starting from the definition of the Sumudu transform on a general time scale, we define the generalized discrete Sumudu transform and present some of its basic properties.
Fahd Jarad, Kenan Taş
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Fractional Calculus for Non-Discrete Signed Measures
MathematicsIn this paper, we suggest a first-ever construction of fractional integral and differential operators based on signed measures including a vector-valued case. The study focuses on constructing the fractional power of the Riemann–Stieltjes integral with a
Vassili N. Kolokoltsov +1 more
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Fractal and Fractional, 2023 Variable-order fractional discrete calculus is a new and unexplored part of calculus that provides extraordinary capabilities for simulating multidisciplinary processes. Recognizing this incredible potential, the scientific community has been researching
Tareq Hamadneh +5 more
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Fractal and Fractional, 2023 In the last few years, reaction–diffusion models associated with discrete fractional calculus have risen in prominence in scientific fields, not just due to the requirement for numerical simulation but also due to the described biological phenomena. This
Tareq Hamadneh +5 more
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