Fractional Mean-Square Inequalities for (P, m)-Superquadratic Stochastic Processes and Their Applications to Stochastic Divergence Measures
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| Pubblicato in: | Fractal and Fractional vol. 9, no. 12 (2025), p. 771-804 |
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| Altri autori: | , , , |
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MDPI AG
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| Accesso online: | Citation/Abstract Full Text + Graphics Full Text - PDF |
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| 022 | |a 2504-3110 | ||
| 024 | 7 | |a 10.3390/fractalfract9120771 |2 doi | |
| 035 | |a 3286294584 | ||
| 045 | 2 | |b d20250101 |b d20251231 | |
| 100 | 1 | |a Khan, Dawood |u Department of Mathematics, University of Balochistan, Quetta 87300, Pakistan; dawooddawood601@gmail.com | |
| 245 | 1 | |a Fractional Mean-Square Inequalities for (P, m)-Superquadratic Stochastic Processes and Their Applications to Stochastic Divergence Measures | |
| 260 | |b MDPI AG |c 2025 | ||
| 513 | |a Journal Article | ||
| 520 | 3 | |a In this study, we introduce and rigorously formalize the notion of (P, m)-superquadratic stochastic processes, representing a novel and far-reaching generalization of classical convex stochastic processes. By exploring their intrinsic structural characteristics, we establish advanced Jensen and Hermite–Hadamard (<inline-formula>H.H</inline-formula>)-type inequalities within the mean-square stochastic calculus framework. Furthermore, we extend these inequalities to their fractional counterparts via stochastic Riemann–Liouville (<inline-formula>RL</inline-formula>) fractional integrals, thereby enriching the analytical machinery available for fractional stochastic analysis. The theoretical findings are comprehensively validated through graphical visualizations and detailed tabular illustrations, constructed from diverse numerical examples to highlight the behavior and accuracy of the proposed results. Beyond their theoretical depth, the developed framework is applied to information theory, where we introduce new classes of stochastic divergence measures. The proposed results significantly refine the approximation of stochastic and fractional stochastic differential equations governed by convex stochastic processes, thereby enhancing the precision, stability, and applicability of existing stochastic models. To ensure reproducibility and computational transparency, all graph-generation commands, numerical procedures, and execution times are provided, offering a complete and verifiable reference for future research in stochastic and fractional inequality theory. | |
| 653 | |a Cryptography | ||
| 653 | |a Control theory | ||
| 653 | |a Calculus | ||
| 653 | |a Divergence | ||
| 653 | |a Stochastic processes | ||
| 653 | |a Inequalities | ||
| 653 | |a Mathematical analysis | ||
| 653 | |a Computer science | ||
| 653 | |a Random variables | ||
| 653 | |a Mathematical models | ||
| 653 | |a Integrals | ||
| 653 | |a Design | ||
| 653 | |a Convex analysis | ||
| 653 | |a Stochastic models | ||
| 653 | |a Engineering | ||
| 653 | |a Mathematics | ||
| 653 | |a Fractional calculus | ||
| 653 | |a Information theory | ||
| 653 | |a Differential equations | ||
| 653 | |a Data compression | ||
| 700 | 1 | |a Butt, Saad Ihsan |u Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore 54000, Pakistan; saadihsanbutt@gmail.com (S.I.B.); fa23-pmt-002@cuilahore.edu.pk (G.J.) | |
| 700 | 1 | |a Jallani Ghulam |u Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore 54000, Pakistan; saadihsanbutt@gmail.com (S.I.B.); fa23-pmt-002@cuilahore.edu.pk (G.J.) | |
| 700 | 1 | |a Alammar Mohammed |u Applied College, Shaqra University, Shaqra 11961, Saudi Arabia; alammar@su.edu.sa | |
| 700 | 1 | |a Seol Youngsoo |u Department of Mathematics, Dong-A University, Busan 49315, Republic of Korea | |
| 773 | 0 | |t Fractal and Fractional |g vol. 9, no. 12 (2025), p. 771-804 | |
| 786 | 0 | |d ProQuest |t Engineering Database | |
| 856 | 4 | 1 | |3 Citation/Abstract |u https://www.proquest.com/docview/3286294584/abstract/embedded/75I98GEZK8WCJMPQ?source=fedsrch |
| 856 | 4 | 0 | |3 Full Text + Graphics |u https://www.proquest.com/docview/3286294584/fulltextwithgraphics/embedded/75I98GEZK8WCJMPQ?source=fedsrch |
| 856 | 4 | 0 | |3 Full Text - PDF |u https://www.proquest.com/docview/3286294584/fulltextPDF/embedded/75I98GEZK8WCJMPQ?source=fedsrch |