Well-posed conditions on a class of fractional q-differential equations by using the Schauder fixed point theorem

Well-posed conditions on a class of fractional q-differential equations by using the Schauder fixed point theorem

Abstract In this paper, we propose the conditions on which a class of boundary value problems, presented by fractional q-differential equations, is well-posed. First, under the suitable conditions, we will prove the existence and uniqueness of solution by means of the Schauder fixed point theorem. T...

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Main Authors: Mohammad Esmael Samei, Ahmad Ahmadi, A. George Maria Selvam, Jehad Alzabut, Shahram Rezapour
Format: article
Language:EN
Published: SpringerOpen 2021
Subjects:
Fractional q-derivative equations
Nonlinear analysis theorems
Well-posedness
Mathematics
QA1-939
Online Access:https://doaj.org/article/287958b78b32476e807cc7c7ecfc6e81
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spelling oai:doaj.org-article:287958b78b32476e807cc7c7ecfc6e812021-11-07T12:13:11ZWell-posed conditions on a class of fractional q-differential equations by using the Schauder fixed point theorem10.1186/s13662-021-03631-21687-1847https://doaj.org/article/287958b78b32476e807cc7c7ecfc6e812021-11-01T00:00:00Zhttps://doi.org/10.1186/s13662-021-03631-2https://doaj.org/toc/1687-1847Abstract In this paper, we propose the conditions on which a class of boundary value problems, presented by fractional q-differential equations, is well-posed. First, under the suitable conditions, we will prove the existence and uniqueness of solution by means of the Schauder fixed point theorem. Then, the stability of solution will be discussed under the perturbations of boundary condition, a function existing in the problem, and the fractional order derivative. Examples involving algorithms and illustrated graphs are presented to demonstrate the validity of our theoretical findings.Mohammad Esmael SameiAhmad AhmadiA. George Maria SelvamJehad AlzabutShahram RezapourSpringerOpenarticleFractional q-derivative equationsNonlinear analysis theoremsWell-posednessMathematicsQA1-939ENAdvances in Difference Equations, Vol 2021, Iss 1, Pp 1-26 (2021)
institution DOAJ
collection DOAJ
language EN
topic Fractional q-derivative equations
Nonlinear analysis theorems
Well-posedness
Mathematics
QA1-939
spellingShingle Fractional q-derivative equations
Nonlinear analysis theorems
Well-posedness
Mathematics
QA1-939
Mohammad Esmael Samei
Ahmad Ahmadi
A. George Maria Selvam
Jehad Alzabut
Shahram Rezapour
Well-posed conditions on a class of fractional q-differential equations by using the Schauder fixed point theorem
description Abstract In this paper, we propose the conditions on which a class of boundary value problems, presented by fractional q-differential equations, is well-posed. First, under the suitable conditions, we will prove the existence and uniqueness of solution by means of the Schauder fixed point theorem. Then, the stability of solution will be discussed under the perturbations of boundary condition, a function existing in the problem, and the fractional order derivative. Examples involving algorithms and illustrated graphs are presented to demonstrate the validity of our theoretical findings.
format article
author Mohammad Esmael Samei
Ahmad Ahmadi
A. George Maria Selvam
Jehad Alzabut
Shahram Rezapour
author_facet Mohammad Esmael Samei
Ahmad Ahmadi
A. George Maria Selvam
Jehad Alzabut
Shahram Rezapour
author_sort Mohammad Esmael Samei
title Well-posed conditions on a class of fractional q-differential equations by using the Schauder fixed point theorem
title_short Well-posed conditions on a class of fractional q-differential equations by using the Schauder fixed point theorem
title_full Well-posed conditions on a class of fractional q-differential equations by using the Schauder fixed point theorem
title_fullStr Well-posed conditions on a class of fractional q-differential equations by using the Schauder fixed point theorem
title_full_unstemmed Well-posed conditions on a class of fractional q-differential equations by using the Schauder fixed point theorem
title_sort well-posed conditions on a class of fractional q-differential equations by using the schauder fixed point theorem
publisher SpringerOpen
publishDate 2021
url https://doaj.org/article/287958b78b32476e807cc7c7ecfc6e81
work_keys_str_mv AT mohammadesmaelsamei wellposedconditionsonaclassoffractionalqdifferentialequationsbyusingtheschauderfixedpointtheorem
AT ahmadahmadi wellposedconditionsonaclassoffractionalqdifferentialequationsbyusingtheschauderfixedpointtheorem
AT ageorgemariaselvam wellposedconditionsonaclassoffractionalqdifferentialequationsbyusingtheschauderfixedpointtheorem
AT jehadalzabut wellposedconditionsonaclassoffractionalqdifferentialequationsbyusingtheschauderfixedpointtheorem
AT shahramrezapour wellposedconditionsonaclassoffractionalqdifferentialequationsbyusingtheschauderfixedpointtheorem
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