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Journals / Advances in the Theory of Nonlinear Analysis and its Application / 2019 / Cilt: 3 - Sayı: 1

Existence and uniqueness of solutions for nonlinear implicit Caputo-Hadamard fractional differential equations with nonlocal conditions

Abdelouaheb ARDJOUNİ
Ahcene DJOUDİ
Pages
46–52
Publication Date
2019-03-31
DOI
—
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AI Summary & Key Takeaways

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

We also use the generalization of Gronwall's inequality to show the estimate of the solutions.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we use the contraction mapping principle to obtain the existence, interval of existence and uniqueness of solutions for nonlinear implicit Caputo-Hadamard fractional differential equations with nonlocal conditions.
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Key Findings & Data:In this paper, we use the contraction mapping principle to obtain the existence, interval of existence and uniqueness of solutions for nonlinear implicit Caputo-Hadamard fractional differential equations with nonlocal conditions.
💡
Conclusion & Impact:We also use the generalization of Gronwall's inequality to show the estimate of the solutions.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Implicit fractional differential equations · Nonlocal conditions · Caputo-Hadamard fractional derivatives

Abstract

In this paper, we use the contraction mapping principle to obtain the existence, interval of existence and uniqueness of solutions for nonlinear implicit Caputo-Hadamard fractional differential equations with nonlocal conditions. We also use the generalization of Gronwall's inequality to show the estimate of the solutions.

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Cite This Article

ARDJOUNİ, A., DJOUDİ, A. (2019). Existence and uniqueness of solutions for nonlinear implicit Caputo-Hadamard fractional differential equations with nonlocal conditions. Advances in the Theory of Nonlinear Analysis and its Application, Cilt: 3 - Sayı: 1, 46–52. https://ajindex.com/articles/729159

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