Positive Solvability for Conjugate Fractional Differential Inclusion of (<i>k</i>, <i>n</i> − <i>k</i>) Type without Continuity and Compactness

Positive Solvability for Conjugate Fractional Differential Inclusion of (<i>k</i>, <i>n</i> − <i>k</i>) Type without Continuity and Compactness

The monotonicity of multi-valued operators serves as a guideline to prove the existence of the results in this article. This theory focuses on the existence of solutions without continuity and compactness conditions. We study these results for the <inline-formula><math xmlns="http://ww...

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Main Authors: Ahmed Salem, Aeshah Al-Dosari
Format: Article
Language:English
Published: MDPI AG 2021-07-01
Series:Axioms
Subjects:
(<i>n</i> − <i>k</i>, <i>k</i>) conjugate operator
existence and uniqueness
monotone operator
spectral radius
Online Access:https://www.mdpi.com/2075-1680/10/3/170
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record_format Article
spelling doaj-adc6f84fcbff41bfafc6b1262002b8882021-09-25T23:44:46ZengMDPI AGAxioms2075-16802021-07-011017017010.3390/axioms10030170Positive Solvability for Conjugate Fractional Differential Inclusion of (<i>k</i>, <i>n</i> − <i>k</i>) Type without Continuity and CompactnessAhmed Salem0Aeshah Al-Dosari1Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaDepartment of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaThe monotonicity of multi-valued operators serves as a guideline to prove the existence of the results in this article. This theory focuses on the existence of solutions without continuity and compactness conditions. We study these results for the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>k</mi><mo>,</mo><mspace width="3.33333pt"></mspace><mi>n</mi><mo>−</mo><mi>k</mi><mo>)</mo></mrow></semantics></math></inline-formula> conjugate fractional differential inclusion type with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="sans-serif">λ</mi><mo>></mo><mn>0</mn><mo>,</mo><mspace width="3.33333pt"></mspace><mn>1</mn><mo>≤</mo><mi>k</mi><mo>≤</mo><mi>n</mi><mo>−</mo><mn>1</mn></mrow></semantics></math></inline-formula>.https://www.mdpi.com/2075-1680/10/3/170(<i>n</i> − <i>k</i>, <i>k</i>) conjugate operatorexistence and uniquenessmonotone operatorspectral radius
collection DOAJ
language English
format Article
sources DOAJ
author Ahmed Salem
Aeshah Al-Dosari
spellingShingle Ahmed Salem
Aeshah Al-Dosari
Positive Solvability for Conjugate Fractional Differential Inclusion of (<i>k</i>, <i>n</i> − <i>k</i>) Type without Continuity and Compactness
Axioms
(<i>n</i> − <i>k</i>, <i>k</i>) conjugate operator
existence and uniqueness
monotone operator
spectral radius
author_facet Ahmed Salem
Aeshah Al-Dosari
author_sort Ahmed Salem
title Positive Solvability for Conjugate Fractional Differential Inclusion of (<i>k</i>, <i>n</i> − <i>k</i>) Type without Continuity and Compactness
title_short Positive Solvability for Conjugate Fractional Differential Inclusion of (<i>k</i>, <i>n</i> − <i>k</i>) Type without Continuity and Compactness
title_full Positive Solvability for Conjugate Fractional Differential Inclusion of (<i>k</i>, <i>n</i> − <i>k</i>) Type without Continuity and Compactness
title_fullStr Positive Solvability for Conjugate Fractional Differential Inclusion of (<i>k</i>, <i>n</i> − <i>k</i>) Type without Continuity and Compactness
title_full_unstemmed Positive Solvability for Conjugate Fractional Differential Inclusion of (<i>k</i>, <i>n</i> − <i>k</i>) Type without Continuity and Compactness
title_sort positive solvability for conjugate fractional differential inclusion of (<i>k</i>, <i>n</i> − <i>k</i>) type without continuity and compactness
publisher MDPI AG
series Axioms
issn 2075-1680
publishDate 2021-07-01
description The monotonicity of multi-valued operators serves as a guideline to prove the existence of the results in this article. This theory focuses on the existence of solutions without continuity and compactness conditions. We study these results for the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>k</mi><mo>,</mo><mspace width="3.33333pt"></mspace><mi>n</mi><mo>−</mo><mi>k</mi><mo>)</mo></mrow></semantics></math></inline-formula> conjugate fractional differential inclusion type with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="sans-serif">λ</mi><mo>></mo><mn>0</mn><mo>,</mo><mspace width="3.33333pt"></mspace><mn>1</mn><mo>≤</mo><mi>k</mi><mo>≤</mo><mi>n</mi><mo>−</mo><mn>1</mn></mrow></semantics></math></inline-formula>.
topic (<i>n</i> − <i>k</i>, <i>k</i>) conjugate operator
existence and uniqueness
monotone operator
spectral radius
url https://www.mdpi.com/2075-1680/10/3/170
work_keys_str_mv AT ahmedsalem positivesolvabilityforconjugatefractionaldifferentialinclusionofikiiniikitypewithoutcontinuityandcompactness
AT aeshahaldosari positivesolvabilityforconjugatefractionaldifferentialinclusionofikiiniikitypewithoutcontinuityandcompactness
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