Some new fixed point results in rectangular metric spaces with an application to fractional-order functional differential equations
Articles
Lokesh Budhia
Sardal Vallabhbhai National Institute of Technology
Hassen Aydi
Ton Duc Thang University
https://orcid.org/0000-0003-4606-7211
Arslan Hojat Ansari
Islamic Azad University
Dhananjay Gopal
Sardal Vallabhbhai National Institute of Technology
Published 2020-07-01
https://doi.org/10.15388/namc.2020.25.17928
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Keywords

fixed point
rectangular metric
nonlinear fractional differential equation

How to Cite

BudhiaL., AydiH., AnsariA. H. and GopalD. (2020) “Some new fixed point results in rectangular metric spaces with an application to fractional-order functional differential equations”, Nonlinear Analysis: Modelling and Control, 25(4), pp. 580–597. doi: 10.15388/namc.2020.25.17928.

Abstract

In this paper, we establish some new fixed point theorems for generalized ϕψ-contractive mappings satisfying an admissibility-type condition in a Hausdorff rectangular metric space with the help of C-functions. In this process, we rectify the proof of Theorem 3.2 due to Budhia et al. [New fixed point results in rectangular metric space and application to fractional calculus, Tbil. Math. J., 10(1):91–104, 2017]. Some examples are given to illustrate the theorems. Finally, we apply our result (Corollary 3.6) to establish the existence of a solution for an initial value problem of a fractional-order functional differential equation with infinite delay. 

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