Existence–Uniqueness and Wright Stability Results of the Riemann–Liouville Fractional Equations by Random Controllers in MB-Spaces

Existence–Uniqueness and Wright Stability Results of the Riemann–Liouville Fractional Equations by Random Controllers in MB-Spaces

We apply the random controllers to stabilize pseudo Riemann–Liouville fractional equations in MB-spaces and investigate existence and uniqueness of their solutions. Next, we compute the optimum error of the estimate. The mentioned process i.e., stabilization by a control function and finding an appr...

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Main Authors: Radko Mesiar, Reza Saadati
Format: Article
Language:English
Published: MDPI AG 2021-07-01
Series:Mathematics
Subjects:
Riemann–Liouville fractional equation
integro-differential equation
MB-spaces
wright stability
fixed point method
Online Access:https://www.mdpi.com/2227-7390/9/14/1602
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spelling doaj-010dbca0f605497898368587a9aad6b62021-07-23T13:52:20ZengMDPI AGMathematics2227-73902021-07-0191602160210.3390/math9141602Existence–Uniqueness and Wright Stability Results of the Riemann–Liouville Fractional Equations by Random Controllers in MB-SpacesRadko Mesiar0Reza Saadati1Faculty of Civil Engineering, Slovak University of Technology, Radlinského 11, 810 05 Bratislava, SlovakiaSchool of Mathematics, Iran University of Science and Technology, Narmak, Tehran 16844, IranWe apply the random controllers to stabilize pseudo Riemann–Liouville fractional equations in MB-spaces and investigate existence and uniqueness of their solutions. Next, we compute the optimum error of the estimate. The mentioned process i.e., stabilization by a control function and finding an approximation for a pseudo functional equation is called random HUR stability. We use a fixed point technique derived from the alternative fixed point theorem (FPT) to investigate random HUR stability of the Riemann–Liouville fractional equations in MB-spaces. As an application, we introduce a class of random Wright control function and investigate existence–uniqueness and Wright stability of these equations in MB-spaces.https://www.mdpi.com/2227-7390/9/14/1602Riemann–Liouville fractional equationintegro-differential equationMB-spaceswright stabilityfixed point method
collection DOAJ
language English
format Article
sources DOAJ
author Radko Mesiar
Reza Saadati
spellingShingle Radko Mesiar
Reza Saadati
Existence–Uniqueness and Wright Stability Results of the Riemann–Liouville Fractional Equations by Random Controllers in MB-Spaces
Mathematics
Riemann–Liouville fractional equation
integro-differential equation
MB-spaces
wright stability
fixed point method
author_facet Radko Mesiar
Reza Saadati
author_sort Radko Mesiar
title Existence–Uniqueness and Wright Stability Results of the Riemann–Liouville Fractional Equations by Random Controllers in MB-Spaces
title_short Existence–Uniqueness and Wright Stability Results of the Riemann–Liouville Fractional Equations by Random Controllers in MB-Spaces
title_full Existence–Uniqueness and Wright Stability Results of the Riemann–Liouville Fractional Equations by Random Controllers in MB-Spaces
title_fullStr Existence–Uniqueness and Wright Stability Results of the Riemann–Liouville Fractional Equations by Random Controllers in MB-Spaces
title_full_unstemmed Existence–Uniqueness and Wright Stability Results of the Riemann–Liouville Fractional Equations by Random Controllers in MB-Spaces
title_sort existence–uniqueness and wright stability results of the riemann–liouville fractional equations by random controllers in mb-spaces
publisher MDPI AG
series Mathematics
issn 2227-7390
publishDate 2021-07-01
description We apply the random controllers to stabilize pseudo Riemann–Liouville fractional equations in MB-spaces and investigate existence and uniqueness of their solutions. Next, we compute the optimum error of the estimate. The mentioned process i.e., stabilization by a control function and finding an approximation for a pseudo functional equation is called random HUR stability. We use a fixed point technique derived from the alternative fixed point theorem (FPT) to investigate random HUR stability of the Riemann–Liouville fractional equations in MB-spaces. As an application, we introduce a class of random Wright control function and investigate existence–uniqueness and Wright stability of these equations in MB-spaces.
topic Riemann–Liouville fractional equation
integro-differential equation
MB-spaces
wright stability
fixed point method
url https://www.mdpi.com/2227-7390/9/14/1602
work_keys_str_mv AT radkomesiar existenceuniquenessandwrightstabilityresultsoftheriemannliouvillefractionalequationsbyrandomcontrollersinmbspaces
AT rezasaadati existenceuniquenessandwrightstabilityresultsoftheriemannliouvillefractionalequationsbyrandomcontrollersinmbspaces
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