EXISTENCE AND STABILITY RESULTS TO A CLASS OF FRACTIONAL RANDOM IMPLICIT DIFFERENTIAL EQUATIONS INVOLVING A GENERALIZED HILFER FRACTIONAL DERIVATIVE

FAHD JARAD; SUGUMARAN HARIKRISHNAN; KAMAL SHAH; KUPPUSAMY KANAGARAJAN

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EXISTENCE AND STABILITY RESULTS TO A CLASS OF FRACTIONAL RANDOM IMPLICIT DIFFERENTIAL EQUATIONS INVOLVING A GENERALIZED HILFER FRACTIONAL DERIVATIVE

机译：存在和稳定性导致一类小数随机隐式微分方程，涉及广义的Hilfer分数衍生物

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In this paper, the existence, uniqueness and stability of random implicit fractional differential equations (RIFDs) with nonlocal condition and impulsive effect involving a generalized Hilfer fractional derivative (HFD) are discussed. The arguments are discussed via Krasnoselskii's fixed point theorems, Schaefer's fixed point theorems, Banach contraction principle and Ulam type stability. Some examples are included to ensure the abstract results.

机译：本文讨论了随机隐式分数微分方程（rifds）的存在，唯一性和稳定性，所述非局部条件和涉及广义的Hilfer分数衍生物（HFD）的脉冲效果。通过Krasnoselskii的定理，Schaefer的定理定理，Banach收缩原理和ulam类型稳定性讨论了争论。包括一些示例以确保抽象结果。

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《Discrete and continuous dynamical systems▼hSeries S》 |2020年第3期|723-739|共17页
作者
FAHD JARAD; SUGUMARAN HARIKRISHNAN; KAMAL SHAH; KUPPUSAMY KANAGARAJAN;
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作者单位

Department of Mathematics Faculty of Arts and Sciences Cankaya University 06790 Ankara Turkey;

Sri Ramakrishna Mission Vidyalaya College of Arts and Science Coimbatore-641020 India;

Department of Mathematics University of Malakand Dir(L)Khyber Pakhtunkhwa Pakistan;

Department of Mathematics University of Malakand Dir(L)Khyber Pakhtunkhwa Pakistan;

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正文语种 eng
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关键词
Random implicit differential equations; generalized Hilfer fractional derivative; existence; uniqueness and stability;

机译：随机隐式微分方程;广义的Hiler Fractional衍生物;存在;唯一性和稳定性;

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1. Asymptotic Stability for Implicit Differential Equations Involving Hilfer Fractional Derivative [J] . Sa?d Abbas, Mouffak Benchohra, Mohamed Abdalla Darwish, Panamerican mathematical journal . 2017,第3期

机译：隐式微分方程的渐近稳定性，涉及HILFER分数衍生物
2. PERIODIC BOUNDARY VALUE PROBLEMS FOR FRACTIONAL IMPLICIT DIFFERENTIAL EQUATIONS INVOLVING HILFER FRACTIONAL DERIVATIVE [J] . Progress in Artificial Intelligence . 2020,第2期

机译：涉及Hilfer分数衍生的分数隐式微分方程的周期边值问题
3. Existence Results for a Nonlocal Coupled System of Sequential Fractional Differential Equations Involving -Hilfer Fractional Derivatives [J] . Athasit Wongcharoen, Sotiris K. Ntouyas, Phollakrit Wongsantisuk, Advances in Mathematical Physics . 2021,第a期

机译：涉及涉及 - 涉及的序列分数衍生物的连续分数差分方程的非识别耦合系统的存在结果
4. Existence of Solutions for Fractional Langevin Equation Involving Generalized Caputo Derivative with Periodic Boundary Conditions [C] . Amita Devi, Anoop Kumar International Conference on Recent Advances in Mathematics Sciences and its Applications . 2020

机译：具有周期边界条件的广义Caputo衍生物的分数Langevin方程解决方案存在
5. Fractional derivatives, fractional differential equations, and their numerical approximation [D] . Hatcher, Christopher 2013

机译：分数阶导数，分数阶微分方程及其数值逼近
6. Existence Results for a System of Coupled Hybrid Fractional Differential Equations [O] . Bashir Ahmad, Sotiris K. Ntouyas, Ahmed Alsaedi -1

机译：一类混合分数阶微分方程组的存在性结果。
7. Stability Results for Implicit Fractional Pantograph Differential Equations via ϕ-Hilfer Fractional Derivative with a Nonlocal Riemann-Liouville Fractional Integral Condition [O] . Idris Ahmed, Poom Kumam, Kamal Shah, 2020

机译：通过φ-hilfer分数衍生物具有非本体riemann-liouville分数整体条件的φ-hilfer分数衍生物的隐式分数耦合仪微分方程的稳定性结果

EXISTENCE AND STABILITY RESULTS TO A CLASS OF FRACTIONAL RANDOM IMPLICIT DIFFERENTIAL EQUATIONS INVOLVING A GENERALIZED HILFER FRACTIONAL DERIVATIVE

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