Convergence of a refined iterative method and its application to fractional Volterra–Fredholm integro-differential equations

Alam, Khairul Habib; Rohen, Yumnam

doi:10.1007/s40314-024-02964-4

Comp. Appl. Math.

2024

DOI: 10.1007/s40314-024-02964-4

|View full text |Cite

Convergence of a refined iterative method and its application to fractional Volterra–Fredholm integro-differential equations

Khairul Habib Alam,

Yumnam Rohen

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2024

Publication Types

Select...

Article2

Relationship

Self Cite0

Independent2

Authors

Journals

Cited by 2 publications

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

Research on inter-plant weeding control in peanut at LADRC based on IACO-PSO optimization

Zhang,

Xu,

Liu

et al. 2024

AIP Advances

View full text Add to dashboard Cite

In the complex operating environments encountered in the field, control system parameters are often difficult to adjust, leading to issues such as excessive overshoot and poor anti-interference performance. These challenges make mechanical seedling avoidance and inter-plant weeding between peanut plants problematic, increasing the risk of seedling damage. To address this, this study investigated a Linear Active Disturbance Rejection Control (LADRC) system for peanut inter-plant weeding, optimized using an improved Ant Colony Optimization-Particle Swarm Optimization IACO-PSO algorithm. By controlling the angular velocity of the stepper motor, we were able to regulate seedling avoidance along the weeding knife’s operational path. A mathematical model for inter-plant seedling avoidance and weeding was established, and an improved hybrid algorithm combining the ant colony algorithm and particle swarm optimization was proposed to optimize the key parameters of the LADRC system. Benchmark function comparisons demonstrated that the improved algorithm offers a superior optimization performance and stability. Simulation experiments were then carried out to evaluate the control performance of the system in the inter-plant weeding scenario. The results show that, compared to other algorithms, the hybrid IACO-PSO algorithm exhibits faster convergence speeds and higher accuracy, significantly enhancing the system’s overall control performance. In particular, the IACO-PSO optimized control system reduced recovery times from disturbances by 96.6%, 75%, 82%, and 64.3%, respectively. These findings highlight the system’s strong anti-interference capability, robustness, and improved response speed, making it a highly effective solution for peanut inter-plant weeding.

show abstract

Research on inter-plant weeding control in peanut at LADRC based on IACO-PSO optimization

Zhang,

Xu,

Liu

et al. 2024

AIP Advances

View full text Add to dashboard Cite

show abstract

A Novel and Efficient Iterative Approach to Approximating Solutions of Fractional Differential Equations

Filali,

Eljaneid,

Alatawi

et al. 2024

Mathematics

View full text Add to dashboard Cite

This study presents a novel and efficient iterative approach to approximating the fixed points of contraction mappings in Banach spaces, specifically approximating the solutions of nonlinear fractional differential equations of the Caputo type. We establish two theorems proving the stability and convergence of the proposed method, supported by numerical examples and graphical comparisons, which indicate a faster convergence rate compared to existing methods, including those by Agarwal, Gursoy, Thakur, Ali and Ali, and D∗∗. Additionally, a data dependence result for approximate operators using the proposed method is provided. This approach is applied to achieve the solutions for Caputo-type fractional differential equations with boundary conditions, demonstrating the efficacy of the method in practical applications.

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

Convergence of a refined iterative method and its application to fractional Volterra–Fredholm integro-differential equations

Cited by 2 publications

References 21 publications

Research on inter-plant weeding control in peanut at LADRC based on IACO-PSO optimization

Research on inter-plant weeding control in peanut at LADRC based on IACO-PSO optimization

A Novel and Efficient Iterative Approach to Approximating Solutions of Fractional Differential Equations

Contact Info

Product

Resources

About