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Ulam–Hyers stability of pantograph fractional stochastic differential equations
Mathematical Methods in the Applied Sciences, 2022In this paper, we investigate the existence and uniqueness theorem (EUT) of Pantograph fractional stochastic differential equations (PFSDE) using the Banach fixed point theorem (BFPT). We show the Ulam–Hyers stability (UHS) of PFSDE by the generalized Gronwall inequalities (GGI). We illustrate our results by two examples.
Lassaad Mchiri +2 more
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Vieta–Fibonacci wavelets: Application in solving fractional pantograph equations
Mathematical Methods in the Applied Sciences, 2021In this paper, the Vieta–Fibonacci wavelets as a new family of orthonormal wavelets are generated. An operational matrix concerning fractional integration of these wavelets is extracted. A numerical scheme is established based on these wavelets and their fractional integral matrix together with the collocation technique to solve fractional pantograph ...
Hadis Azin +2 more
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New stability theorem for uncertain pantograph differential equations
Journal of Intelligent & Fuzzy Systems, 2021Uncertain pantograph differential equation (UPDE for short) is a special unbounded uncertain delay differential equation. Stability in measure, stability almost surely and stability in p-th moment for uncertain pantograph differential equation have been investigated, which are not applicable for all situations, for the sake of completeness, this paper ...
Jia, Zhifu, Liu, Xinsheng, Zhang, Yu
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Pantograph stochastic differential equations driven by G-Brownian motion
Journal of Mathematical Analysis and Applications, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hu, Lanying, Ren, Yong, He, Qian
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Long time numerical behaviors of fractional pantograph equations
Mathematics and Computers in Simulation, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Li, Dongfang, Zhang, Chengjian
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Existence of solutions of nonlinear fractional pantograph equations
Acta Mathematica Scientia, 2013Abstract This article deals with the existence of solutions of nonlinear fractional pantograph equations. Such model can be considered suitable to be applied when the corresponding process occurs through strongly anomalous media. The results are obtained using fractional calculus and fixed point theorems. An example is provided to illustrate the main
K. BALACHANDRAN +2 more
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Neural network solution of pantograph type differential equations
Mathematical Methods in the Applied Sciences, 2020We investigate the approximate solution of pantograph type functional differential equations using neural networks. The methodology is based on the ideas of Lagaris et al, and itis applied to various problems with a proportional delay term subject to initial or boundary conditions. The proposed methodology proves to be very efficient.
Chih‐Chun Hou +2 more
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Existence Results for Nonlinear Hilfer Pantograph Fractional Integrodifferential Equations
Qualitative Theory of Dynamical SystemszbMATH Open Web Interface contents unavailable due to conflicting licenses.
Radhakrishnan, B. +4 more
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Generalized polynomial chaos for nonlinear random pantograph equations
Acta Mathematicae Applicatae Sinica, English Series, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Shi, Wen-Jie, Zhang, Cheng-Jian
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Strong Predictor-Corrector Methods for Stochastic Pantograph Equations
Journal of Computational Mathematics, 2018The paper introduces a new class of numerical schemes for the approximate solutions of stochastic pantograph equations. As an effective technique to implement implicit stochastic methods, strong predictor-corrector methods (PCMs) are designed to handle scenario simulation of solutions of stochastic pantograph equations.
Feiyan Xiao, Peng Wang
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