Approximate Solutions of an Extended Multi-Order Boundary Value Problem by Implementing Two Numerical Algorithms

Approximate Solutions of an Extended Multi-Order Boundary Value Problem by Implementing Two Numerical Algorithms

In this paper, we establish several necessary conditions to confirm the uniqueness-existence of solutions to an extended multi-order finite-term fractional differential equation with double-order integral boundary conditions with respect to asymmetric operators by relying on the Banach’s fixed-point...

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Bibliographic Details
Main Authors: Surang Sitho, Sina Etemad, Brahim Tellab, Shahram Rezapour, Sotiris K. Ntouyas, Jessada Tariboon
Format: Article
Language:English
Published: MDPI AG 2021-07-01
Series:Symmetry
Subjects:
approximate solutions
boundary value problem
existence
Riemann–Liouville derivative
Online Access:https://www.mdpi.com/2073-8994/13/8/1341
Description
Summary:In this paper, we establish several necessary conditions to confirm the uniqueness-existence of solutions to an extended multi-order finite-term fractional differential equation with double-order integral boundary conditions with respect to asymmetric operators by relying on the Banach’s fixed-point criterion. We validate our study by implementing two numerical schemes to handle some Riemann–Liouville fractional boundary value problems and obtain approximate series solutions that converge to the exact ones. In particular, we present several examples that illustrate the closeness of the approximate solutions to the exact solutions.
ISSN:2073-8994

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