SavedAdd your journal

Journals / Hacettepe Journal of Mathematics and Statistics / 2013 / Cilt: 42 - Sayı: 2

UNIQUENESS RESULTS AND CONVERGENCE OF SUCCESSIVE APPROXIMATIONS FOR FRACTIONAL DIFFERENTIAL EQUATIONS

Jun WU
Yicheng LİU
Pages
149–158
Publication Date
2022-10-18
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Our methodsare based on the equivalent norm techniques and fixed point theorem.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we establish some existence and uniqueness results foran initial value problem with a Caputo fractional derivative.
📊
Key Findings & Data:Also, theconvergence of successive approximations is exhibited.
💡
Conclusion & Impact:Our methodsare based on the equivalent norm techniques and fixed point theorem.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Fractional differential equations · Krasnoselskii-Krein type condition · Equivalent norm.

Abstract

In this paper, we establish some existence and uniqueness results foran initial value problem with a Caputo fractional derivative. Also, theconvergence of successive approximations is exhibited. Our methodsare based on the equivalent norm techniques and fixed point theorem.

🔖

Cite This Article

WU, J., LİU, Y. (2022). UNIQUENESS RESULTS AND CONVERGENCE OF SUCCESSIVE APPROXIMATIONS FOR FRACTIONAL DIFFERENTIAL EQUATIONS. Hacettepe Journal of Mathematics and Statistics, Cilt: 42 - Sayı: 2, 149–158. https://ajindex.com/articles/530425

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (6)

  1. Agarwal, R.P., Zhou, Y., He, Y., Existence of fractional neutral functional differential equations, Computers and Mathematics with Applications, In Press.
  2. Ahmad, B., Nieto, J.J., Existence of solutions for nonlocal boundary value problems of higher-order nonlinear fractional differential equations, Abstract and Applied Analysis, 200 Arara A. el al., Fractional order differential equations on an unbounded domain, Nonlinear Anal. TMA (in press). Belmekki, M., Nieto, J.J., Rodriguez-Lopez, R., Existence of Periodic Solution for a Nonlinear Fractional Differential Equation, Boundary Value Problems, 2009.
  3. Bhaskar, T. G., Lakshmikantham, V., Leela, S., Fractional differential equations with Krasnoselskii-Krein-type condition, Nonlinear Analysis: Hybrid Systems, 2009.
  4. Lakshmikantham, V., Leela, S., Nagumo-type uniqueness result for fractional differential equations, Nonlinear Analysis 71, 2886-2889, 2009.
  5. Lakshmikantham, V., Leela, S., A Krasnoselskii-Krein-type uniqueness result for fractional differential equations, Nonlinear Analysis 71, 3421-3424, 2009.
  6. Lakshmikantham, V., Leela, S., Vasundhara Devi J., Theory of Fractional Dynamic Systems, Cambridge Scientific Publishers, 2009.