Qualitative Analysis of Multi-Terms Fractional Order Delay Differential Equations via the Topological Degree Theory

Qualitative Analysis of Multi-Terms Fractional Order Delay Differential Equations via the Topological Degree Theory

With the help of the topological degree theory in this manuscript, we develop qualitative theory for a class of multi-terms fractional order differential equations (FODEs) with proportional delay using the Caputo derivative. In the same line, we will also study various forms of Ulam stability result...

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Main Authors: Muhammad Sher, Kamal Shah, Michal Fečkan, Rahmat Ali Khan
Format: Article
Language:English
Published: MDPI AG 2020-02-01
Series:Mathematics
Subjects:
fractional differential equations
existence and uniqueness of solutions
topological degree method
Online Access:https://www.mdpi.com/2227-7390/8/2/218
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spelling doaj-94a4725b5def403b9874be7952c2f5382020-11-25T01:30:16ZengMDPI AGMathematics2227-73902020-02-018221810.3390/math8020218math8020218Qualitative Analysis of Multi-Terms Fractional Order Delay Differential Equations via the Topological Degree TheoryMuhammad Sher0Kamal Shah1Michal Fečkan2Rahmat Ali Khan3Department of Mathematics, University of Malakand, Dir(L), Khyber Pakhtunkhwa 18000, PakistanDepartment of Mathematics, University of Malakand, Dir(L), Khyber Pakhtunkhwa 18000, PakistanDepartment of Mathematical Analysis and Numerical Mathematics, Faculty of Mathematics, Physics and Informatics, Comenius University in Bratislava, Mlynská Dolina, 842 48 Bratislava, SlovakiaDepartment of Mathematics, University of Malakand, Dir(L), Khyber Pakhtunkhwa 18000, PakistanWith the help of the topological degree theory in this manuscript, we develop qualitative theory for a class of multi-terms fractional order differential equations (FODEs) with proportional delay using the Caputo derivative. In the same line, we will also study various forms of Ulam stability results. To clarify our theocratical analysis, we provide three different pertinent examples.https://www.mdpi.com/2227-7390/8/2/218fractional differential equationsexistence and uniqueness of solutionstopological degree method
collection DOAJ
language English
format Article
sources DOAJ
author Muhammad Sher
Kamal Shah
Michal Fečkan
Rahmat Ali Khan
spellingShingle Muhammad Sher
Kamal Shah
Michal Fečkan
Rahmat Ali Khan
Qualitative Analysis of Multi-Terms Fractional Order Delay Differential Equations via the Topological Degree Theory
Mathematics
fractional differential equations
existence and uniqueness of solutions
topological degree method
author_facet Muhammad Sher
Kamal Shah
Michal Fečkan
Rahmat Ali Khan
author_sort Muhammad Sher
title Qualitative Analysis of Multi-Terms Fractional Order Delay Differential Equations via the Topological Degree Theory
title_short Qualitative Analysis of Multi-Terms Fractional Order Delay Differential Equations via the Topological Degree Theory
title_full Qualitative Analysis of Multi-Terms Fractional Order Delay Differential Equations via the Topological Degree Theory
title_fullStr Qualitative Analysis of Multi-Terms Fractional Order Delay Differential Equations via the Topological Degree Theory
title_full_unstemmed Qualitative Analysis of Multi-Terms Fractional Order Delay Differential Equations via the Topological Degree Theory
title_sort qualitative analysis of multi-terms fractional order delay differential equations via the topological degree theory
publisher MDPI AG
series Mathematics
issn 2227-7390
publishDate 2020-02-01
description With the help of the topological degree theory in this manuscript, we develop qualitative theory for a class of multi-terms fractional order differential equations (FODEs) with proportional delay using the Caputo derivative. In the same line, we will also study various forms of Ulam stability results. To clarify our theocratical analysis, we provide three different pertinent examples.
topic fractional differential equations
existence and uniqueness of solutions
topological degree method
url https://www.mdpi.com/2227-7390/8/2/218
work_keys_str_mv AT muhammadsher qualitativeanalysisofmultitermsfractionalorderdelaydifferentialequationsviathetopologicaldegreetheory
AT kamalshah qualitativeanalysisofmultitermsfractionalorderdelaydifferentialequationsviathetopologicaldegreetheory
AT michalfeckan qualitativeanalysisofmultitermsfractionalorderdelaydifferentialequationsviathetopologicaldegreetheory
AT rahmatalikhan qualitativeanalysisofmultitermsfractionalorderdelaydifferentialequationsviathetopologicaldegreetheory
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