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Mathematics
Article . 2023 . Peer-reviewed
License: CC BY
Data sources: Crossref
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Mathematics
Article . 2023
Data sources: DOAJ
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q-Fractional Langevin Differential Equation with q-Fractional Integral Conditions

Authors: Wuyang Wang; Khansa Hina Khalid; Akbar Zada; Sana Ben Moussa; Jun Ye;

q-Fractional Langevin Differential Equation with q-Fractional Integral Conditions

Abstract

The major goal of this manuscript is to investigate the existence, uniqueness, and stability of a q-fractional Langevin differential equation with q-fractional integral conditions. We demonstrate the existence and uniqueness of the solution to the proposed q-fractional Langevin differential equation using the Banach contraction principle and Schaefer’s fixed-point theorem. We also elaborate on different kinds of Ulam stability. The theoretical outcomes are verified by examples.

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Keywords

Langevin equations; fractional <i>q</i>-differential equation; Caputo derivative; green function; Ulam stability, Ulam stability, QA1-939, fractional <i>q</i>-differential equation, Langevin equations, green function, Caputo derivative, Mathematics

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    5
    popularity
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    Top 10%
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
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    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
    Top 10%
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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
5
Top 10%
Average
Top 10%
gold