Peano Theorems for Pedjeu–Ladde-Type Multi-Time Scale Stochastic Differential Equations Driven by Fractional Noises
This paper examines fractional multi-time scale stochastic functional differential equations that, in addition, are driven by fractional noises. Based on a specially crafted fixed-point principle for the so-called “local operators”, we prove a Peano-type theorem on the existence of weak solutions, t...
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2025-01-01
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| author | Arcady Ponosov Lev Idels |
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| description | This paper examines fractional multi-time scale stochastic functional differential equations that, in addition, are driven by fractional noises. Based on a specially crafted fixed-point principle for the so-called “local operators”, we prove a Peano-type theorem on the existence of weak solutions, that is, those defined on an extended stochastic basis. To encompass all commonly used particular classes of fractional multi-time scale stochastic models, including those with random delays and impulses at random times, we consider equations with nonlinear random Volterra operators rather than functions. Some crucial properties of the associated integral operators, needed for the proofs of the main results, are studied as well. To illustrate major findings, several existence theorems, generalizing those known in the literature, are offered, with the emphasis put on the most popular examples such as ordinary stochastic differential equations driven by fractional noises, fractional stochastic differential equations with variable delays and fractional stochastic neutral differential equations. |
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| institution | Kabale University |
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| language | English |
| publishDate | 2025-01-01 |
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| spelling | doaj-art-9a3bea0b944c48ccb83493bfc23d9fac2025-01-24T13:39:44ZengMDPI AGMathematics2227-73902025-01-0113220410.3390/math13020204Peano Theorems for Pedjeu–Ladde-Type Multi-Time Scale Stochastic Differential Equations Driven by Fractional NoisesArcady Ponosov0Lev Idels1Department of Mathematics, Norwegian University of Life Sciences, 1432 Aas, NorwayDepartment of Mathematics, Vancouver Island University, 900 Fifth St., Nanaimo, BC V9S 5S5, CanadaThis paper examines fractional multi-time scale stochastic functional differential equations that, in addition, are driven by fractional noises. Based on a specially crafted fixed-point principle for the so-called “local operators”, we prove a Peano-type theorem on the existence of weak solutions, that is, those defined on an extended stochastic basis. To encompass all commonly used particular classes of fractional multi-time scale stochastic models, including those with random delays and impulses at random times, we consider equations with nonlinear random Volterra operators rather than functions. Some crucial properties of the associated integral operators, needed for the proofs of the main results, are studied as well. To illustrate major findings, several existence theorems, generalizing those known in the literature, are offered, with the emphasis put on the most popular examples such as ordinary stochastic differential equations driven by fractional noises, fractional stochastic differential equations with variable delays and fractional stochastic neutral differential equations.https://www.mdpi.com/2227-7390/13/2/204fixed-point principlefractional calculusmulti-time scalesPeano’s theoremstochastic differential equationsVolterra operators |
| spellingShingle | Arcady Ponosov Lev Idels Peano Theorems for Pedjeu–Ladde-Type Multi-Time Scale Stochastic Differential Equations Driven by Fractional Noises Mathematics fixed-point principle fractional calculus multi-time scales Peano’s theorem stochastic differential equations Volterra operators |
| title | Peano Theorems for Pedjeu–Ladde-Type Multi-Time Scale Stochastic Differential Equations Driven by Fractional Noises |
| title_full | Peano Theorems for Pedjeu–Ladde-Type Multi-Time Scale Stochastic Differential Equations Driven by Fractional Noises |
| title_fullStr | Peano Theorems for Pedjeu–Ladde-Type Multi-Time Scale Stochastic Differential Equations Driven by Fractional Noises |
| title_full_unstemmed | Peano Theorems for Pedjeu–Ladde-Type Multi-Time Scale Stochastic Differential Equations Driven by Fractional Noises |
| title_short | Peano Theorems for Pedjeu–Ladde-Type Multi-Time Scale Stochastic Differential Equations Driven by Fractional Noises |
| title_sort | peano theorems for pedjeu ladde type multi time scale stochastic differential equations driven by fractional noises |
| topic | fixed-point principle fractional calculus multi-time scales Peano’s theorem stochastic differential equations Volterra operators |
| url | https://www.mdpi.com/2227-7390/13/2/204 |
| work_keys_str_mv | AT arcadyponosov peanotheoremsforpedjeuladdetypemultitimescalestochasticdifferentialequationsdrivenbyfractionalnoises AT levidels peanotheoremsforpedjeuladdetypemultitimescalestochasticdifferentialequationsdrivenbyfractionalnoises |