Study of Hybrid Problems under Exponential Type Fractional-Order Derivatives

IF 1.3 4区 数学 Q1 MATHEMATICS Journal of Mathematics Pub Date : 2024-05-29 DOI:10.1155/2024/2274198
Mohammed S. Abdo, Sahar Ahmed Idris, M. Daher Albalwi, Tomadir Ahmed Idris
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Abstract

In this investigation, we develop a theory for the hybrid boundary value problem for fractional differential equations subject to three-point boundary conditions, including the antiperiodic hybrid boundary condition. On suggested problems, the third-order Caputo–Fabrizio derivative is the fractional operator applied. In this regard, the corresponding hybrid fractional integral equation is obtained by the Caputo–Fabrizio operator’s properties with the Green function’s aid. Then, we apply Dhage’s nonlinear alternative to the Schaefer type to prove the existence results. Finally, two examples are provided to confirm the validity of our main results.
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指数型分阶导数下的混合问题研究
在这项研究中,我们发展了受三点边界条件(包括反周期混合边界条件)限制的分数微分方程的混合边界值问题理论。在建议的问题中,三阶 Caputo-Fabrizio 导数是应用的分数算子。在这方面,利用卡普托-法布里齐奥算子的性质和格林函数的辅助,可以得到相应的混合分数积分方程。然后,我们应用 Dhage 的非线性替代 Schaefer 类型来证明存在性结果。最后,我们提供了两个例子来证实我们主要结果的正确性。
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来源期刊
Journal of Mathematics
Journal of Mathematics Mathematics-General Mathematics
CiteScore
2.50
自引率
14.30%
发文量
0
期刊介绍: Journal of Mathematics is a broad scope journal that publishes original research articles as well as review articles on all aspects of both pure and applied mathematics. As well as original research, Journal of Mathematics also publishes focused review articles that assess the state of the art, and identify upcoming challenges and promising solutions for the community.
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