Applications to Nonlinear Fractional Differential Equations via Common Fixed Point on ℂ★-Algebra-Valued Bipolar Metric Spaces

Gunaseelan Mani; Arul Joseph Gnanaprakasam; Poornavel Subbarayan; Subramanian Chinnachamy; Reny George; Zoran D. Mitrović

doi:10.3390/fractalfract7070534

Applications to Nonlinear Fractional Differential Equations via Common Fixed Point on ℂ^★-Algebra-Valued Bipolar Metric Spaces

Gunaseelan Mani
, Arul Joseph Gnanaprakasam
, Poornavel Subbarayan
, Subramanian Chinnachamy
, Reny George
, Zoran D. Mitrović

Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

In the present paper, we prove common fixed point theorems under different contractive mappings on (Formula presented.) -algebra-valued bipolar metric spaces. The results generalize and expand some well-known results from the literature. Examples and applications are given to strengthen our conclusion. Additionally, as an application of our results, we show that some classes of the nonlinear fractional differential equations with the boundary conditions have a unique common solution.

Original language	English
Article number	534
Journal	Fractal and Fractional
Volume	7
Issue number	7
DOIs	https://doi.org/10.3390/fractalfract7070534
State	Published - Jul 2023

Keywords

bipolar metric space
common fixed point
fractional differential equation
ℂ-algebra
ℂ-algebra-valued bipolar metric space

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10.3390/fractalfract7070534

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title = "Applications to Nonlinear Fractional Differential Equations via Common Fixed Point on ℂ★-Algebra-Valued Bipolar Metric Spaces",

abstract = "In the present paper, we prove common fixed point theorems under different contractive mappings on (Formula presented.) -algebra-valued bipolar metric spaces. The results generalize and expand some well-known results from the literature. Examples and applications are given to strengthen our conclusion. Additionally, as an application of our results, we show that some classes of the nonlinear fractional differential equations with the boundary conditions have a unique common solution.",

keywords = "bipolar metric space, common fixed point, fractional differential equation, ℂ-algebra, ℂ-algebra-valued bipolar metric space",

author = "Gunaseelan Mani and Gnanaprakasam, \{Arul Joseph\} and Poornavel Subbarayan and Subramanian Chinnachamy and Reny George and Mitrovi{\'c}, \{Zoran D.\}",

note = "Publisher Copyright: {\textcopyright} 2023 by the authors.",

year = "2023",

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doi = "10.3390/fractalfract7070534",

language = "English",

volume = "7",

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T1 - Applications to Nonlinear Fractional Differential Equations via Common Fixed Point on ℂ★-Algebra-Valued Bipolar Metric Spaces

AU - Mani, Gunaseelan

AU - Gnanaprakasam, Arul Joseph

AU - Subbarayan, Poornavel

AU - Chinnachamy, Subramanian

AU - George, Reny

AU - Mitrović, Zoran D.

PY - 2023/7

Y1 - 2023/7

N2 - In the present paper, we prove common fixed point theorems under different contractive mappings on (Formula presented.) -algebra-valued bipolar metric spaces. The results generalize and expand some well-known results from the literature. Examples and applications are given to strengthen our conclusion. Additionally, as an application of our results, we show that some classes of the nonlinear fractional differential equations with the boundary conditions have a unique common solution.

AB - In the present paper, we prove common fixed point theorems under different contractive mappings on (Formula presented.) -algebra-valued bipolar metric spaces. The results generalize and expand some well-known results from the literature. Examples and applications are given to strengthen our conclusion. Additionally, as an application of our results, we show that some classes of the nonlinear fractional differential equations with the boundary conditions have a unique common solution.

KW - bipolar metric space

KW - common fixed point

KW - fractional differential equation

KW - ℂ-algebra

KW - ℂ-algebra-valued bipolar metric space

UR - https://www.scopus.com/pages/publications/85175103424

U2 - 10.3390/fractalfract7070534

DO - 10.3390/fractalfract7070534

M3 - Article

AN - SCOPUS:85175103424

SN - 2504-3110

VL - 7

JO - Fractal and Fractional

JF - Fractal and Fractional

IS - 7

M1 - 534

ER -

Applications to Nonlinear Fractional Differential Equations via Common Fixed Point on ℂ^★-Algebra-Valued Bipolar Metric Spaces

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Keywords

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