On the Existence and Uniqueness of the Solution of a Nonlinear Fractional Differential Equation with Integral Boundary Condition

IF 1.4 4区 物理与天体物理 Q2 MATHEMATICS, APPLIED
Elyas Shivanian
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引用次数: 0

Abstract

Abstract This study focuses on investigating the existence and uniqueness of a solution to a specific type of high-order nonlinear fractional differential equations that include the Rieman-Liouville fractional derivative. The boundary condition is of integral type, which involves both the starting and ending points of the domain. Initially, the unique exact solution is derived using Green’s function for the linear fractional differential equation. Subsequently, the Banach contraction mapping theorem is employed to establish the main result for the general nonlinear source term case. Moreover, an illustrative example is presented to demonstrate the legitimacy and applicability of our main result.
一类具有积分边界条件的非线性分数阶微分方程解的存在唯一性
摘要研究一类含Rieman-Liouville分数阶导数的高阶非线性分数阶微分方程解的存在唯一性。边界条件为积分型,既包括域的起点,也包括域的终点。首先,利用格林函数推导出线性分数阶微分方程的唯一精确解。随后,利用Banach收缩映射定理建立了一般非线性源项情况下的主要结果。最后,通过实例验证了本文主要结论的合理性和适用性。
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来源期刊
Journal of Nonlinear Mathematical Physics
Journal of Nonlinear Mathematical Physics PHYSICS, MATHEMATICAL-PHYSICS, MATHEMATICAL
CiteScore
1.60
自引率
0.00%
发文量
67
审稿时长
3 months
期刊介绍: Journal of Nonlinear Mathematical Physics (JNMP) publishes research papers on fundamental mathematical and computational methods in mathematical physics in the form of Letters, Articles, and Review Articles. Journal of Nonlinear Mathematical Physics is a mathematical journal devoted to the publication of research papers concerned with the description, solution, and applications of nonlinear problems in physics and mathematics. The main subjects are: -Nonlinear Equations of Mathematical Physics- Quantum Algebras and Integrability- Discrete Integrable Systems and Discrete Geometry- Applications of Lie Group Theory and Lie Algebras- Non-Commutative Geometry- Super Geometry and Super Integrable System- Integrability and Nonintegrability, Painleve Analysis- Inverse Scattering Method- Geometry of Soliton Equations and Applications of Twistor Theory- Classical and Quantum Many Body Problems- Deformation and Geometric Quantization- Instanton, Monopoles and Gauge Theory- Differential Geometry and Mathematical Physics
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