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Title
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On the existence of solutions for nonlocal sequential boundary fractional differential equations via $\psi$-Riemann-Liouville derivative
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Type
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JournalPaper
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Keywords
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Sequential $\psi$-Riemann-Liouville fractional differential equation; nonlinear differential systems; existence and uniqueness; Lyapunov-type inequality;Banach's contraction principle
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Abstract
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The purpose of this paper is to study a generalized Riemann-Liouville fractional differential equation and system with nonlocal boundary conditions. Firstly, some properties of the Green function are presented, and then establish Lyapunov-type inequalities for a sequential $\psi$-Riemann-Liouville fractional boundary value problem. Also, the existence and uniqueness of solutions are proved by using Banach and Schauder fixed point theorems. Furthermore, the existence and uniqueness of solutions to a sequential nonlinear differential system is established by means of Schauder's and Perov's fixed point theorems. Examples are given to validate the theoretical results.
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Researchers
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Mohammad Esmael Samei (Second Researcher), Faouzi Haddouchi (First Researcher)
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