Existence, uniqueness, and averaging principle for Hadamard Itô–Doob stochastic delay fractional integral equations

Mchiri, Lassaad; Mtiri, Foued

doi:10.1002/mma.9346

Cited by 2 publications

(1 citation statement)

References 23 publications

(32 reference statements)

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“…Ahmad et al [40] investigated a coupled system of Hilfer-Hadamard fractional equations. Ben Makhlouf et al [41] studied the existence, uniqueness, and averaging principle for Hadamard Ito-Doob stochastic delay fractional integral equations. Briefly, the properties, research approaches, and generalization of the concept of H-derivative, as well as the effects of delay, impulse, and random factors on H-fractional differential systems, have always attracted the attention of scholars.…”

Section: Remark 2 When Boundary Conditionsmentioning

confidence: 99%

A Unified Approach to Solvability and Stability of Multipoint BVPs for Langevin and Sturm–Liouville Equations with CH–Fractional Derivatives and Impulses via Coincidence Theory

Zhao,

Liu,

2024

Fractal Fract

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The Langevin equation is a model for describing Brownian motion, while the Sturm–Liouville equation is an important mechanical model. This paper focuses on the solvability and stability of nonlinear impulsive Langevin and Sturm–Liouville equations with Caputo–Hadamard (CH) fractional derivatives and multipoint boundary value conditions. To unify the two types of equations, we investigate a general nonlinear impulsive coupled implicit system. By cleverly constructing relevant operators involving impulsive terms, we establish the coincidence degree theory and obtain the solvability. We explore the stability of solutions using nonlinear analysis and inequality techniques. As the most direct application, we naturally obtained the solvability and stability of the Langevin and Sturm–Liouville equations mentioned above. Finally, an example is provided to demonstrate the validity and availability of our major findings.

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Section: Remark 2 When Boundary Conditionsmentioning

confidence: 99%

A Unified Approach to Solvability and Stability of Multipoint BVPs for Langevin and Sturm–Liouville Equations with CH–Fractional Derivatives and Impulses via Coincidence Theory

Zhao,

Liu,

2024

Fractal Fract

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Computational analysis of the Covid-19 model using the continuous Galerkin–Petrov scheme

Naz,

Jan,

Attaullah

et al. 2024

Nonlinear Engineering

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Epidemiological models feature reliable and valuable insights into the prevention and transmission of life-threatening illnesses. In this study, a novel SIR mathematical model for COVID-19 is formulated and examined. The newly developed model has been thoroughly explored through theoretical analysis and computational methods, specifically the continuous Galerkin–Petrov (cGP) scheme. The next-generation matrix approach was used to calculate the reproduction number ( R 0 ) ({R}_{0}) . Both disease-free equilibrium (DFE) ( E 0 ) ({E}^{0}) and the endemic equilibrium ( E ⁎ ) ({E}^{\ast }) points are derived for the proposed model. The stability analysis of the equilibrium points reveals that ( E 0 ) ({E}^{0}) is locally asymptotically stable when R 0 < 1 {R}_{0}\lt 1 , while E ⁎ {E}^{\ast } is globally asymptotically stable when R 0 > 1 {R}_{0}\gt 1 . We have examined the model’s local stability (LS) and global stability (GS) for endemic equilibrium \text{ } and DFE based on the number ( R 0 ) ({R}_{0}) . To ascertain the dominance of the parameters, we examined the sensitivity of the number ( R 0 ) ({R}_{0}) to parameters and computed sensitivity indices. Additionally, using the fourth-order Runge–Kutta (RK4) and Runge–Kutta–Fehlberg (RK45) techniques implemented in MATLAB, we determined the numerical solutions. Furthermore, the model was solved using the continuous cGP time discretization technique. We implemented a variety of schemes like cGP(2), RK4, and RK45 for the COVID-19 model and presented the numerical and graphical solutions of the model. Furthermore, we compared the results obtained using the above-mentioned schemes and observed that all results overlap with each other. The significant properties of several physical parameters under consideration were discussed. In the end, the computational analysis shows a clear image of the rise and fall in the spread of this disease over time in a specific location.

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Existence, uniqueness, and averaging principle for Hadamard Itô–Doob stochastic delay fractional integral equations

Cited by 2 publications

References 23 publications

A Unified Approach to Solvability and Stability of Multipoint BVPs for Langevin and Sturm–Liouville Equations with CH–Fractional Derivatives and Impulses via Coincidence Theory

A Unified Approach to Solvability and Stability of Multipoint BVPs for Langevin and Sturm–Liouville Equations with CH–Fractional Derivatives and Impulses via Coincidence Theory

Computational analysis of the Covid-19 model using the continuous Galerkin–Petrov scheme

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