Application of Fixed Points in Bipolar Controlled Metric Space to Solve Fractional Differential Equation

Gunaseelan Mani; Rajagopalan Ramaswamy; Arul Joseph Gnanaprakasam; Amr Elsonbaty; Ola A.Ashour Abdelnaby; Stojan Radenović

doi:10.3390/fractalfract7030242

Application of Fixed Points in Bipolar Controlled Metric Space to Solve Fractional Differential Equation

Gunaseelan Mani, Rajagopalan Ramaswamy, Arul Joseph Gnanaprakasam, Amr Elsonbaty, Ola A.Ashour Abdelnaby, Stojan Radenović

Mathematics

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

14 Scopus citations

Abstract

Fixed point results and metric fixed point theory play a vital role to find the unique solution to differential and integral equations. Likewise, fractal calculus has vast physical applications. In this article, we introduce the concept of bipolar-controlled metric space and prove fixed point theorems. The derived results expand and extend certain well-known results from the research literature and are supported with a non-trivial example. We have applied the fixed point result to find the analytical solution to the integral equation and fractional differential equation. The analytical solution has been supplemented with numerical simulation.

Original language	English
Article number	242
Journal	Fractal and Fractional
Volume	7
Issue number	3
DOIs	https://doi.org/10.3390/fractalfract7030242
State	Published - Mar 2023

Keywords

bipolar metric space
bipolar-controlled metric space
contravariant map
covariant map
fixed point

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10.3390/fractalfract7030242

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abstract = "Fixed point results and metric fixed point theory play a vital role to find the unique solution to differential and integral equations. Likewise, fractal calculus has vast physical applications. In this article, we introduce the concept of bipolar-controlled metric space and prove fixed point theorems. The derived results expand and extend certain well-known results from the research literature and are supported with a non-trivial example. We have applied the fixed point result to find the analytical solution to the integral equation and fractional differential equation. The analytical solution has been supplemented with numerical simulation.",

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AU - Mani, Gunaseelan

AU - Ramaswamy, Rajagopalan

AU - Gnanaprakasam, Arul Joseph

AU - Elsonbaty, Amr

AU - Abdelnaby, Ola A.Ashour

AU - Radenović, Stojan

PY - 2023/3

Y1 - 2023/3

N2 - Fixed point results and metric fixed point theory play a vital role to find the unique solution to differential and integral equations. Likewise, fractal calculus has vast physical applications. In this article, we introduce the concept of bipolar-controlled metric space and prove fixed point theorems. The derived results expand and extend certain well-known results from the research literature and are supported with a non-trivial example. We have applied the fixed point result to find the analytical solution to the integral equation and fractional differential equation. The analytical solution has been supplemented with numerical simulation.

AB - Fixed point results and metric fixed point theory play a vital role to find the unique solution to differential and integral equations. Likewise, fractal calculus has vast physical applications. In this article, we introduce the concept of bipolar-controlled metric space and prove fixed point theorems. The derived results expand and extend certain well-known results from the research literature and are supported with a non-trivial example. We have applied the fixed point result to find the analytical solution to the integral equation and fractional differential equation. The analytical solution has been supplemented with numerical simulation.

KW - bipolar metric space

KW - bipolar-controlled metric space

KW - contravariant map

KW - covariant map

KW - fixed point

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ER -

Application of Fixed Points in Bipolar Controlled Metric Space to Solve Fractional Differential Equation

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Keywords

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