α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}-Whittaker controllability of ϑ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\vartheta $$\end{document}-Hilfer fractional stochastic evolution equations driven by fractional Brownian motion

被引：0

作者：

Mohammad Bagher Ghaemi

Fatemeh Mottaghi

Reza Saadati

Tofigh Allahviranloo

机构：

[1] Iran University of Science and Technology,School of Mathematics

[2] Istinye University,Faculty of Engineering and Natural Sciences

来源：

Computational and Applied Mathematics | 2023年 / 42卷 / 5期

关键词：

-Hilfer fractional derivative; Stochastic evolution equations; Fractional Brownian motion; Controllability; Whittaker function; Economic growth model; Ramsey model; 45E10; 65R20;

D O I：

10.1007/s40314-023-02357-z

中图分类号：

学科分类号：

摘要：

In this paper, we study the fractional-order system in the sense of ϑ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\vartheta $$\end{document}-Hilfer fractional stochastic evolution equations driven by fractional Brownian motion. Applying the fixed point technique, we prove that there exists a mild solution for the problem and introduce a new type of stability. Finally, we present two examples to demonstrate how the obtained results might be applied.

引用

共 41 条

[31] Numerical Scheme for Stochastic Differential Equations Driven by Fractional Brownian Motion with 1/4<H<1/2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ 1/4<H <1/2$$\end{document}.
Héctor Araya
Jorge A. León
Soledad Torres
Journal of Theoretical Probability, 2020, 33 (3) : 1211 - 1237
[32] Controllability and semigroups of invariant control systems on Sln,H\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm {Sl}}\left( n,{\mathbb {H}}\right) $$\end{document}
Bruno A. Rodrigues
Luiz A. B. San Martin
Alexandre J. Santana
Mathematics of Control, Signals, and Systems, 2022, 34 (2) : 393 - 404
[33] Existence and Uniqueness of Strong Solutions of Mixed-Type Stochastic Differential Equations Driven by Fractional Brownian Motions with Hurst Exponents \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H>1/4 $$\end{document}
M. M. Vas’kovskii
P. P. Stryuk
Differential Equations, 2024, 60 (6) : 691 - 702
[34] Measure theory and S2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S^{2}$$\end{document}-pseudo almost periodic and automorphic process: application to stochastic evolution equations
Mamadou Abdoul Diop
Khalil Ezzinbi
Mamadou Moustapha Mbaye
Afrika Matematika, 2015, 26 (5-6) : 779 - 812
[35] New best proximity point (pair) theorems via MNC and application to the existence of optimum solutions for a system of ψ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\psi $$\end{document}-Hilfer fractional differential equations
Pradip Ramesh Patle
Moosa Gabeleh
Vladimir Rakočević
Mohammad Esmael Samei
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2023, 117 (3):
[36] Controllability Analysis of Neutral Stochastic Differential Equation Using ψ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\psi $$\end{document}-Hilfer Fractional Derivative with Rosenblatt ProcessControllability Analysis of Neutral Stochastic...M. Lavanya et al.
M. Lavanya
B. Sundara Vadivoo
Kottakkaran Sooppy Nisar
Qualitative Theory of Dynamical Systems, 2025, 24 (1)
[37] Simulation of Weakly Self-Similar Stationary Increment \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{Sub}}_{\varphi } {\left( \Omega \right)}$$\end{document}-Processes: A Series Expansion Approach
Yuriy Kozachenko
Tommi Sottinen
Olga Vasylyk
Methodology and Computing in Applied Probability, 2005, 7 (3) : 379 - 400
[38] Delay Equations with Non-negativity Constraints Driven by a Hölder Continuous Function of Order \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\beta \in \left(\frac13,\frac12\right)$\end{document}
Mireia Besalú
David Márquez-Carreras
Carles Rovira
Potential Analysis, 2014, 41 (1) : 117 - 141
[39] From Constructive Field Theory to Fractional Stochastic Calculus. (II) Constructive Proof of Convergence for the Lévy Area of Fractional Brownian Motion with Hurst Index \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\alpha}\,{\in}\,(\frac{1}{8},\frac{1}{4})}$$\end{document}
Jacques Magnen
Jérémie Unterberger
Annales Henri Poincaré, 2012, 13 (2) : 209 - 270
[40] Controllability of multi-term fractional-order impulsive dynamical systems with φ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varphi $$\end{document}-Caputo fractional derivativeControllability of multi-term fractional-order...Md. S. H. Ansari, M. Malik
Md. Samshad Hussain Ansari
Muslim Malik
Fractional Calculus and Applied Analysis, 2025, 28 (2) : 1040 - 1070

← 1 2 3 4 5 →