Common fixed point theorems for auxiliary functions with applications in fractional differential equation

Ben Wongsaijai

doi:10.1186/s13662-021-03660-x

Common fixed point theorems for auxiliary functions with applications in fractional differential equation

2021-11-22

8

OA

AI

B

Ben Wongsaijai

P

Phakdi Charoensawan

T

Teeranush Suebcharoen

W

Watchareepan Atiponrat *

DOI：10.1186/s13662-021-03660-x

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Abstract

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In this work, we investigate h-phi contraction mappings with two metrics endowed with a directed graph which involve auxiliary functions. The achievement allows us to obtain applications for the existence of the solutions for Caputo fractional boundary value problems with the integral boundary condition type. In addition, we also give examples and numerical experiments supporting our main results.

Keywords:

Fixed point

Common fixed point

Fractional differential equation

Common fixed point theorems for auxiliary functions with applications in fractional differential equation

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