Common and Coincidence Fixed-Point Theorems for ℑ-Contractions with Existence Results for Nonlinear Fractional Differential Equations

Bilal Iqbal; Naeem Saleem; Iram Iqbal; Reny George

doi:10.3390/fractalfract7100747

Common and Coincidence Fixed-Point Theorems for ℑ-Contractions with Existence Results for Nonlinear Fractional Differential Equations

Bilal Iqbal, Naeem Saleem^*, Iram Iqbal, Reny George^*

^*Corresponding author for this work

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

1 Citation (Scopus)

Abstract

In this paper, we derive the coincidence fixed-point and common fixed-point results for ℑ-type mappings satisfying certain contractive conditions and containing fewer conditions imposed on function ℑ with regard to generalized metric spaces (in terms of Jleli Samet). Finally, a fractional boundary value problem is reduced to an equivalent Volterra integral equation, and the existence results of common solutions are obtained with the use of proved fixed-point results.

Original language	English
Article number	747
Journal	Fractal and Fractional
Volume	7
Issue number	10
DOIs	https://doi.org/10.3390/fractalfract7100747
Publication status	Published - Oct 2023
Externally published	Yes

Keywords

coincidence fixed point
common fixed point
fractional differential equation
generalized metric space
integral boundary conditions
ℑ-contraction

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10.3390/fractalfract7100747

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title = "Common and Coincidence Fixed-Point Theorems for ℑ-Contractions with Existence Results for Nonlinear Fractional Differential Equations",

abstract = "In this paper, we derive the coincidence fixed-point and common fixed-point results for ℑ-type mappings satisfying certain contractive conditions and containing fewer conditions imposed on function ℑ with regard to generalized metric spaces (in terms of Jleli Samet). Finally, a fractional boundary value problem is reduced to an equivalent Volterra integral equation, and the existence results of common solutions are obtained with the use of proved fixed-point results.",

keywords = "coincidence fixed point, common fixed point, fractional differential equation, generalized metric space, integral boundary conditions, ℑ-contraction",

author = "Bilal Iqbal and Naeem Saleem and Iram Iqbal and Reny George",

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T1 - Common and Coincidence Fixed-Point Theorems for ℑ-Contractions with Existence Results for Nonlinear Fractional Differential Equations

AU - Iqbal, Bilal

AU - Saleem, Naeem

AU - Iqbal, Iram

AU - George, Reny

PY - 2023/10

Y1 - 2023/10

N2 - In this paper, we derive the coincidence fixed-point and common fixed-point results for ℑ-type mappings satisfying certain contractive conditions and containing fewer conditions imposed on function ℑ with regard to generalized metric spaces (in terms of Jleli Samet). Finally, a fractional boundary value problem is reduced to an equivalent Volterra integral equation, and the existence results of common solutions are obtained with the use of proved fixed-point results.

AB - In this paper, we derive the coincidence fixed-point and common fixed-point results for ℑ-type mappings satisfying certain contractive conditions and containing fewer conditions imposed on function ℑ with regard to generalized metric spaces (in terms of Jleli Samet). Finally, a fractional boundary value problem is reduced to an equivalent Volterra integral equation, and the existence results of common solutions are obtained with the use of proved fixed-point results.

KW - coincidence fixed point

KW - common fixed point

KW - fractional differential equation

KW - generalized metric space

KW - integral boundary conditions

KW - ℑ-contraction

UR - http://www.scopus.com/inward/record.url?scp=85175159523&partnerID=8YFLogxK

U2 - 10.3390/fractalfract7100747

DO - 10.3390/fractalfract7100747

M3 - Article

AN - SCOPUS:85175159523

SN - 2504-3110

VL - 7

JO - Fractal and Fractional

JF - Fractal and Fractional

IS - 10

M1 - 747

ER -

Common and Coincidence Fixed-Point Theorems for ℑ-Contractions with Existence Results for Nonlinear Fractional Differential Equations

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Keywords

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