Separate Fractional (<i>p</i>,<i>q</i>)-Integrodifference Equations via Nonlocal Fractional (<i>p</i>,<i>q</i>)-Integral Boundary Conditions

Separate Fractional (<i>p</i>,<i>q</i>)-Integrodifference Equations via Nonlocal Fractional (<i>p</i>,<i>q</i>)-Integral Boundary Conditions

In this paper, we study a boundary value problem involving <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>...

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Autores principales: Thongchai Dumrongpokaphan, Sotiris K. Ntouyas, Thanin Sitthiwirattham
Formato: article
Lenguaje:EN
Publicado: MDPI AG 2021
Materias:
fractional (<i>p</i>,<i>q</i>)-integral
fractional (<i>p</i>,<i>q</i>)-difference
nonlocal boundary value problems
existence
Mathematics
QA1-939
Acceso en línea:https://doaj.org/article/6426018d69434a37b8d889c77644d7f7
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spelling oai:doaj.org-article:6426018d69434a37b8d889c77644d7f72021-11-25T19:07:37ZSeparate Fractional (<i>p</i>,<i>q</i>)-Integrodifference Equations via Nonlocal Fractional (<i>p</i>,<i>q</i>)-Integral Boundary Conditions10.3390/sym131122122073-8994https://doaj.org/article/6426018d69434a37b8d889c77644d7f72021-11-01T00:00:00Zhttps://www.mdpi.com/2073-8994/13/11/2212https://doaj.org/toc/2073-8994In this paper, we study a boundary value problem involving <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></semantics></math></inline-formula>-integrodifference equations, supplemented with nonlocal fractional <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></semantics></math></inline-formula>-integral boundary conditions with respect to asymmetric operators. First, we convert the given nonlinear problem into a fixed-point problem, by considering a linear variant of the problem at hand. Once the fixed-point operator is available, existence and uniqueness results are established using the classical Banach’s and Schaefer’s fixed-point theorems. The application of the main results is demonstrated by presenting numerical examples. Moreover, we study some properties of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></semantics></math></inline-formula>-integral that are used in our study.Thongchai DumrongpokaphanSotiris K. NtouyasThanin SitthiwiratthamMDPI AGarticlefractional (<i>p</i>,<i>q</i>)-integralfractional (<i>p</i>,<i>q</i>)-differencenonlocal boundary value problemsexistenceMathematicsQA1-939ENSymmetry, Vol 13, Iss 2212, p 2212 (2021)
institution DOAJ
collection DOAJ
language EN
topic fractional (<i>p</i>,<i>q</i>)-integral
fractional (<i>p</i>,<i>q</i>)-difference
nonlocal boundary value problems
existence
Mathematics
QA1-939
spellingShingle fractional (<i>p</i>,<i>q</i>)-integral
fractional (<i>p</i>,<i>q</i>)-difference
nonlocal boundary value problems
existence
Mathematics
QA1-939
Thongchai Dumrongpokaphan
Sotiris K. Ntouyas
Thanin Sitthiwirattham
Separate Fractional (<i>p</i>,<i>q</i>)-Integrodifference Equations via Nonlocal Fractional (<i>p</i>,<i>q</i>)-Integral Boundary Conditions
description In this paper, we study a boundary value problem involving <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></semantics></math></inline-formula>-integrodifference equations, supplemented with nonlocal fractional <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></semantics></math></inline-formula>-integral boundary conditions with respect to asymmetric operators. First, we convert the given nonlinear problem into a fixed-point problem, by considering a linear variant of the problem at hand. Once the fixed-point operator is available, existence and uniqueness results are established using the classical Banach’s and Schaefer’s fixed-point theorems. The application of the main results is demonstrated by presenting numerical examples. Moreover, we study some properties of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></semantics></math></inline-formula>-integral that are used in our study.
format article
author Thongchai Dumrongpokaphan
Sotiris K. Ntouyas
Thanin Sitthiwirattham
author_facet Thongchai Dumrongpokaphan
Sotiris K. Ntouyas
Thanin Sitthiwirattham
author_sort Thongchai Dumrongpokaphan
title Separate Fractional (<i>p</i>,<i>q</i>)-Integrodifference Equations via Nonlocal Fractional (<i>p</i>,<i>q</i>)-Integral Boundary Conditions
title_short Separate Fractional (<i>p</i>,<i>q</i>)-Integrodifference Equations via Nonlocal Fractional (<i>p</i>,<i>q</i>)-Integral Boundary Conditions
title_full Separate Fractional (<i>p</i>,<i>q</i>)-Integrodifference Equations via Nonlocal Fractional (<i>p</i>,<i>q</i>)-Integral Boundary Conditions
title_fullStr Separate Fractional (<i>p</i>,<i>q</i>)-Integrodifference Equations via Nonlocal Fractional (<i>p</i>,<i>q</i>)-Integral Boundary Conditions
title_full_unstemmed Separate Fractional (<i>p</i>,<i>q</i>)-Integrodifference Equations via Nonlocal Fractional (<i>p</i>,<i>q</i>)-Integral Boundary Conditions
title_sort separate fractional (<i>p</i>,<i>q</i>)-integrodifference equations via nonlocal fractional (<i>p</i>,<i>q</i>)-integral boundary conditions
publisher MDPI AG
publishDate 2021
url https://doaj.org/article/6426018d69434a37b8d889c77644d7f7
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AT sotiriskntouyas separatefractionalipiiqiintegrodifferenceequationsvianonlocalfractionalipiiqiintegralboundaryconditions
AT thaninsitthiwirattham separatefractionalipiiqiintegrodifferenceequationsvianonlocalfractionalipiiqiintegralboundaryconditions
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