Fractional Inclusion Analysis of Superquadratic Stochastic Processes via Center-Radius Total Order Relation with Applications in Information Theory
This study presents, for the first time, a new class of interval-valued superquadratic stochastic processes and examines their core properties through the lens of the center-radius total order relation on intervals. These processes serve as a powerful tool for modeling uncertainty in stochastic syst...
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| Format: | Article |
| Language: | English |
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MDPI AG
2025-06-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/9/6/375 |
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| author | Mohsen Ayyash Dawood Khan Saad Ihsan Butt Youngsoo Seol |
| author_facet | Mohsen Ayyash Dawood Khan Saad Ihsan Butt Youngsoo Seol |
| author_sort | Mohsen Ayyash |
| collection | DOAJ |
| description | This study presents, for the first time, a new class of interval-valued superquadratic stochastic processes and examines their core properties through the lens of the center-radius total order relation on intervals. These processes serve as a powerful tool for modeling uncertainty in stochastic systems involving interval-valued data. By utilizing their intrinsic structure, we derive sharpened versions of Jensen-type and Hermite–Hadamard-type inequalities, along with their fractional extensions, within the framework of mean-square stochastic Riemann–Liouville fractional integrals. The theoretical findings are validated through extensive graphical representations and numerical simulations. Moreover, the applicability of the proposed processes is demonstrated in the domain of information theory by constructing novel stochastic divergence measures and Shannon’s entropy grounded in interval calculus. The outcomes of this work lay a solid foundation for further exploration in stochastic analysis, particularly in advancing generalized integral inequalities and formulating new stochastic models under uncertainty. |
| format | Article |
| id | doaj-art-85e5abea355547f6ac67b2d01e233278 |
| institution | OA Journals |
| issn | 2504-3110 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj-art-85e5abea355547f6ac67b2d01e2332782025-08-20T02:21:11ZengMDPI AGFractal and Fractional2504-31102025-06-019637510.3390/fractalfract9060375Fractional Inclusion Analysis of Superquadratic Stochastic Processes via Center-Radius Total Order Relation with Applications in Information TheoryMohsen Ayyash0Dawood Khan1Saad Ihsan Butt2Youngsoo Seol3School of Mathematical Sciences, Universiti Sains Malaysia, Penang 11800, MalaysiaSchool of Mathematical Sciences, Universiti Sains Malaysia, Penang 11800, MalaysiaDepartment of Mathematics, Lahore Campus, COMSATS University Islamabad, Lahore 54000, PakistanDepartment of Mathematics, Dong-A University, Busan 49315, Republic of KoreaThis study presents, for the first time, a new class of interval-valued superquadratic stochastic processes and examines their core properties through the lens of the center-radius total order relation on intervals. These processes serve as a powerful tool for modeling uncertainty in stochastic systems involving interval-valued data. By utilizing their intrinsic structure, we derive sharpened versions of Jensen-type and Hermite–Hadamard-type inequalities, along with their fractional extensions, within the framework of mean-square stochastic Riemann–Liouville fractional integrals. The theoretical findings are validated through extensive graphical representations and numerical simulations. Moreover, the applicability of the proposed processes is demonstrated in the domain of information theory by constructing novel stochastic divergence measures and Shannon’s entropy grounded in interval calculus. The outcomes of this work lay a solid foundation for further exploration in stochastic analysis, particularly in advancing generalized integral inequalities and formulating new stochastic models under uncertainty.https://www.mdpi.com/2504-3110/9/6/375interval calculussuperquadratic stochastic processcenter-radius interval-valued superquadratic stochastic processJensen’s inequalitymean-square stochastic Riemann–Liouville fractional integralsRiemann–Liouville fractional stochastic Hermite–Hadamard divergence |
| spellingShingle | Mohsen Ayyash Dawood Khan Saad Ihsan Butt Youngsoo Seol Fractional Inclusion Analysis of Superquadratic Stochastic Processes via Center-Radius Total Order Relation with Applications in Information Theory Fractal and Fractional interval calculus superquadratic stochastic process center-radius interval-valued superquadratic stochastic process Jensen’s inequality mean-square stochastic Riemann–Liouville fractional integrals Riemann–Liouville fractional stochastic Hermite–Hadamard divergence |
| title | Fractional Inclusion Analysis of Superquadratic Stochastic Processes via Center-Radius Total Order Relation with Applications in Information Theory |
| title_full | Fractional Inclusion Analysis of Superquadratic Stochastic Processes via Center-Radius Total Order Relation with Applications in Information Theory |
| title_fullStr | Fractional Inclusion Analysis of Superquadratic Stochastic Processes via Center-Radius Total Order Relation with Applications in Information Theory |
| title_full_unstemmed | Fractional Inclusion Analysis of Superquadratic Stochastic Processes via Center-Radius Total Order Relation with Applications in Information Theory |
| title_short | Fractional Inclusion Analysis of Superquadratic Stochastic Processes via Center-Radius Total Order Relation with Applications in Information Theory |
| title_sort | fractional inclusion analysis of superquadratic stochastic processes via center radius total order relation with applications in information theory |
| topic | interval calculus superquadratic stochastic process center-radius interval-valued superquadratic stochastic process Jensen’s inequality mean-square stochastic Riemann–Liouville fractional integrals Riemann–Liouville fractional stochastic Hermite–Hadamard divergence |
| url | https://www.mdpi.com/2504-3110/9/6/375 |
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