Integral Inequalities and Differential Equations via Fractional Calculus
In this chapter, fractional calculus is used to develop some results on integral inequalities and differential equations. We develop some results related to the Hermite-Hadamard inequality. Then, we establish other integral results related to the Minkowski inequality. We continue to present our resu...
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Capítulo de libro |
| Lenguaje: | inglés |
| Publicado: |
IntechOpen
2020
|
| Materias: | |
| Acceso en línea: | https://www.intechopen.com/chapters/71053 |
| Etiquetas: |
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1879164695534895104 |
|---|---|
| author | Dahmani, Zoubir Belhamiti, Meriem Mansouria |
| author_browse | Belhamiti, Meriem Mansouria Dahmani, Zoubir |
| author_facet | Dahmani, Zoubir Belhamiti, Meriem Mansouria |
| author_sort | Dahmani, Zoubir |
| building | IntechOpen |
| collection | Acceso abierto |
| description | In this chapter, fractional calculus is used to develop some results on integral inequalities and differential equations. We develop some results related to the Hermite-Hadamard inequality. Then, we establish other integral results related to the Minkowski inequality. We continue to present our results by establishing new classes of fractional integral inequalities using a family of positive functions; these classes of inequalities can be considered as generalizations of order
n
for some other classical/fractional integral results published recently. As applications on inequalities, we generate new lower bounds estimating the fractional expectations and variances for the beta random variable. Some classical covariance identities, which correspond to the classical case, are generalised for any
α
≥
1
,
β
≥
1
. For the part of differential equations, we present a contribution that allow us to develop a class of fractional chaotic electrical circuit. We prove recent results for the existence and uniqueness of solutions for a class of Langevin-type equation. Then, by establishing some sufficient conditions, another result for the existence of at least one solution is also discussed. |
| doi_str_mv | 10.5772/intechopen.91140 |
| first_indexed | 2026-10-15T21:38:26Z |
| format | Book Chapter |
| fullrecord | <oai_dc:dc xmlns:oai_dc="http://www.openarchives.org/OAI/2.0/oai_dc/" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.openarchives.org/OAI/2.0/oai_dc/ http://www.openarchives.org/OAI/2.0/oai_dc.xsd"><identifier>intech-71053</identifier><datestamp>2020-02-12</datestamp>
<dc:title>Integral Inequalities and Differential Equations via Fractional Calculus</dc:title>
<dc:creator>Zoubir Dahmani</dc:creator>
<dc:creator>Meriem Mansouria Belhamiti</dc:creator>
<dc:subject>Physical Sciences, Engineering and Technology</dc:subject>
<dc:description>In this chapter, fractional calculus is used to develop some results on integral inequalities and differential equations. We develop some results related to the Hermite-Hadamard inequality. Then, we establish other integral results related to the Minkowski inequality. We continue to present our results by establishing new classes of fractional integral inequalities using a family of positive functions; these classes of inequalities can be considered as generalizations of order
n
for some other classical/fractional integral results published recently. As applications on inequalities, we generate new lower bounds estimating the fractional expectations and variances for the beta random variable. Some classical covariance identities, which correspond to the classical case, are generalised for any
α
≥
1
,
β
≥
1
. For the part of differential equations, we present a contribution that allow us to develop a class of fractional chaotic electrical circuit. We prove recent results for the existence and uniqueness of solutions for a class of Langevin-type equation. Then, by establishing some sufficient conditions, another result for the existence of at least one solution is also discussed.</dc:description>
<dc:publisher>IntechOpen</dc:publisher>
<dc:date>2020-02-12</dc:date>
<dc:type>Chapter, Part Of Book</dc:type>
<dc:identifier>https://www.intechopen.com/chapters/71053</dc:identifier>
<dc:identifier>doi:10.5772/intechopen.91140</dc:identifier>
<dc:language>en</dc:language>
<dc:relation>ISBN:978-1-83880-007-9</dc:relation>
<dc:rights>https://creativecommons.org/licenses/by/3.0/</dc:rights>
<dc:source>https://www.intechopen.com/books/7785 ; Functional Calculus</dc:source>
</oai_dc:dc> |
| id | intech-71053 |
| institution | IntechOpen |
| isbn | 978-1-83880-007-9 |
| language | English |
| last_indexed | 2026-10-15T21:38:26Z |
| publishDate | 2020 |
| publishDateRange | 2020 |
| publishDateSort | 2020 |
| publisher | IntechOpen |
| publisherStr | IntechOpen |
| record_format | oai_dc |
| spelling | intech-710532020-02-12 Integral Inequalities and Differential Equations via Fractional Calculus Zoubir Dahmani Meriem Mansouria Belhamiti Physical Sciences, Engineering and Technology In this chapter, fractional calculus is used to develop some results on integral inequalities and differential equations. We develop some results related to the Hermite-Hadamard inequality. Then, we establish other integral results related to the Minkowski inequality. We continue to present our results by establishing new classes of fractional integral inequalities using a family of positive functions; these classes of inequalities can be considered as generalizations of order n for some other classical/fractional integral results published recently. As applications on inequalities, we generate new lower bounds estimating the fractional expectations and variances for the beta random variable. Some classical covariance identities, which correspond to the classical case, are generalised for any α ≥ 1 , β ≥ 1 . For the part of differential equations, we present a contribution that allow us to develop a class of fractional chaotic electrical circuit. We prove recent results for the existence and uniqueness of solutions for a class of Langevin-type equation. Then, by establishing some sufficient conditions, another result for the existence of at least one solution is also discussed. IntechOpen 2020-02-12 Chapter, Part Of Book https://www.intechopen.com/chapters/71053 doi:10.5772/intechopen.91140 en ISBN:978-1-83880-007-9 https://creativecommons.org/licenses/by/3.0/ https://www.intechopen.com/books/7785 ; Functional Calculus |
| spellingShingle | Physical Sciences, Engineering and Technology Dahmani, Zoubir Belhamiti, Meriem Mansouria Integral Inequalities and Differential Equations via Fractional Calculus |
| title | Integral Inequalities and Differential Equations via Fractional Calculus |
| title_full | Integral Inequalities and Differential Equations via Fractional Calculus |
| title_fullStr | Integral Inequalities and Differential Equations via Fractional Calculus |
| title_full_unstemmed | Integral Inequalities and Differential Equations via Fractional Calculus |
| title_short | Integral Inequalities and Differential Equations via Fractional Calculus |
| title_sort | integral inequalities and differential equations via fractional calculus |
| topic | Physical Sciences, Engineering and Technology |
| url | https://www.intechopen.com/chapters/71053 |
| work_keys_str_mv | AT dahmanizoubir integralinequalitiesanddifferentialequationsviafractionalcalculus AT belhamitimeriemmansouria integralinequalitiesanddifferentialequationsviafractionalcalculus |