Results 31 to 40 of about 600,406 (168)
Discrete Dynamics in Nature and Society, 2018 The first-order and second-order PDα-type iterative learning control (ILC) schemes are considered for a class of Caputo-type fractional-order nonlinear systems.
Lei Li
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Journal of Inequalities and Applications, 2016 In this paper, we state and prove a new discrete q-fractional version of the Gronwall inequality. Based on this result, a particular version expressed by means of the q-Mittag-Leffler function is provided.
T. Abdeljawad, J. Alzabut, D. Baleanu
semanticscholar +2 more sources
A New Gronwall–Bellman Inequality in Frame of Generalized Proportional Fractional Derivative
Mathematics, 2019 New versions of a Gronwall−Bellman inequality in the frame of the generalized (Riemann−Liouville and Caputo) proportional fractional derivative are provided.
Jehad Alzabut +3 more
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Controllability results of neutral Caputo fractional functional differential equations
AIMS Mathematics, 2023 In this paper, using the properties of the phase space on infinite delay, generalized Gronwall inequality and fixed point theorems, the existence and controllability results of neutral fractional functional differential equations with multi-term Caputo ...
Qi Wang +3 more
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Global stabilization of a Korteweg-de Vries equation with saturating distributed control
, 2016 This article deals with the design of saturated controls in the context of partial differential equations. It focuses on a Korteweg-de Vries equation, which is a nonlinear mathematical model of waves on shallow water surfaces.
Andrieu, Vincent +3 more
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AIMS MathematicsThe Gronwall-Bellman inequality is a primary tool for proving various types of stability. For this importance, the present paper focuses on the generalized forms of the well-known Gronwall-Bellman inequality in the context of the Hadamard fractional ...
Sina Etemad +2 more
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A McKean--Vlasov equation with positive feedback and blow-ups [PDF]
, 2018 We study a McKean--Vlasov equation arising from a mean-field model of a particle system with positive feedback. As particles hit a barrier they cause the other particles to jump in the direction of the barrier and this feedback mechanism leads to the ...
Hambly, Ben +2 more
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The -Fractional Analogue for Gronwall-Type Inequality
Journal of Function Spaces and Applications, 2013 We utilize -fractional Caputo initial value problems of order to derive a -analogue for Gronwall-type inequality. Some particular cases are derived where -Mittag-Leffler functions and -exponential type functions are used.
Thabet Abdeljawad, Jehad O. Alzabut
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On the Hyers-Ulam Stability of Differential Equations of Second Order
Abstract and Applied Analysis, 2014 By using of the Gronwall inequality, we prove the Hyers-Ulam stability of differential equations of second order with initial conditions.
Qusuay H. Alqifiary, Soon-Mo Jung
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A new approach to interval-valued inequalities
Advances in Difference Equations, 2020 The objective of this work is to advance and simplify the notion of Gronwall’s inequality. By using an efficient partial order and concept of gH-differentiability on interval-valued functions, we investigate some new variants of Gronwall type ...
Awais Younus +4 more
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