Rapid Convergence of Approximate Solutions for Fractional Differential Equations

Wu, Xiran; Bao, Junyan; Sun, Yufeng

doi:10.1155/2020/5370524

Journal of Function Spaces

2020

DOI: 10.1155/2020/5370524

|View full text |Cite

Rapid Convergence of Approximate Solutions for Fractional Differential Equations

Xiran Wu

Junyan Bao

Yufeng Sun

Abstract: In this paper, we develop a generalized quasilinearization technique for a class of Caputo’s fractional differential equations when the forcing function is the sum of hyperconvex and hyperconcave functions of order m (m≥0), and we obtain the convergence of the sequences of approximate solutions by establishing the convergence of order k (k≥2).

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...

Article1

Relationship

Self Cite0

Independent1

Authors

Journals

Cited by 1 publication

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

Analysis of multi-term arbitrary order implicit differential equations with variable type delay

ur Rahman,

Wahid,

Gómez-Aguilar

et al. 2024

Phys. Scr.

View full text Add to dashboard Cite

Due to their capacity to simulate intricate dynamic systems containing memory effects and non-local interactions, fractional differential equations have attracted a great deal of attention lately. This study examinesmulti-term fractional differential equations with variable type delay with the goal of illuminating their complex dynamics and analytical characteristics. The introduction to fractional calculus and the justificationfor its use in many scientific and technical domains sets the stage for the remainder of the essay. It describesthe importance of including variable type delay in differential equations and then applying it to model moresophisticated and realistic behaviours of real-world phenomena. The research study then presents the mathematical formulation of variable type delay and multi-term fractional differential equations. The system’snovelty stems from its unique combination of variable delay, generalized multi terms fractional differentialoperators (n and m), and integral implicit parameters, and studying the stability of the the newly formulatedsystem as compared to the work in the existing literature. While the variable type delay is introduced as afunction of time to describe instances where the delay is not constant, the fractional order derivatives aregenerated using the Caputo approach. The existence, uniqueness, and stability of solutions are the maintopics of the theoretical analysis of the suggested differential equations. In order to establish importantmathematical features, the inquiry makes use of spectral techniques, and fixed-point theorems. The studyfinishes by summarizing the major discoveries and outlining potential future research avenues in this developing field. It highlights the potential contribution of multi-term fractional differential equations withvariable type delay to improving the control and design of complex systems. Overall, this study adds to thegrowing body of knowledge in the field of fractional calculus and provides insightful information about theinvestigation of multi-term fractional differential equations.

show abstract

Analysis of multi-term arbitrary order implicit differential equations with variable type delay

ur Rahman,

Wahid,

Gómez-Aguilar

et al. 2024

Phys. Scr.

View full text Add to dashboard Cite

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.

Rapid Convergence of Approximate Solutions for Fractional Differential Equations

Cited by 1 publication

References 27 publications

Analysis of multi-term arbitrary order implicit differential equations with variable type delay

Analysis of multi-term arbitrary order implicit differential equations with variable type delay

Contact Info

Product

Resources

About