On a Riemann–Liouville Type Implicit Coupled System via Generalized Boundary Conditions

On a Riemann–Liouville Type Implicit Coupled System via Generalized Boundary Conditions

We study a coupled system of implicit differential equations with fractional-order differential boundary conditions and the Riemann–Liouville derivative. The existence, uniqueness, and at least one solution are established by applying the Banach contraction and Leray–Schauder fixed point theorem. Fu...

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Bibliographic Details
Main Authors: Usman Riaz, Akbar Zada, Zeeshan Ali, Ioan-Lucian Popa, Shahram Rezapour, Sina Etemad
Format: Article
Language:English
Published: MDPI AG 2021-05-01
Series:Mathematics
Subjects:
Riemann–Liouville fractional derivative
coupled system
fractional order boundary conditions
green function
existence theory
Ulam stability
Online Access:https://www.mdpi.com/2227-7390/9/11/1205
Description
Summary:We study a coupled system of implicit differential equations with fractional-order differential boundary conditions and the Riemann–Liouville derivative. The existence, uniqueness, and at least one solution are established by applying the Banach contraction and Leray–Schauder fixed point theorem. Furthermore, Hyers–Ulam type stabilities are discussed. An example is presented to illustrate our main result. The suggested system is the generalization of fourth-order ordinary differential equations with anti-periodic, classical, and initial boundary conditions.
ISSN:2227-7390

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