Control Fuzzy Metric Spaces via Orthogonality with an Application

Uddin, Fahim; Javed, Khalil; Aydi, Hassen; Ishtiaq, Umar; Arshad, Muhammad

doi:10.1155/2021/5551833

Cited by 20 publications

(12 citation statements)

References 9 publications

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“…is result was generalized in different spaces and different structures were attained using this topic. One may recall some basic results related to this topic, such as controlled fuzzy metric spaces and some related fixed point results in [16], controlled metric type spaces, and the related contraction principle in [17] and orthogonally controlled metric type spaces in [18], and very recently, the new aspects of metric spaces in [19].…”

Section: Introductionmentioning

confidence: 99%

Intuitionistic Fuzzy Double Controlled Metric Spaces and Related Results

Farheen

Ahmed

Javed

et al. 2022

Security and Communication Networks

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In this article, we introduce the concept of intuitionistic fuzzy double controlled metric spaces that generalizes the concept of intuitionistic fuzzy b-metric spaces. For this purpose, two noncomparable functions are used in triangle inequalities. We generalize the concepts of the Banach contraction principle and fuzzy contractive mappings by giving authentic proof of these mappings in the sense of intuitionistic fuzzy double controlled metric spaces. To validate the superiority of these results, examples are imparted. A possible application to solving integral equations is also set forth towards the end of this work to support the proposed results.

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Section: Introductionmentioning

confidence: 99%

Intuitionistic Fuzzy Double Controlled Metric Spaces and Related Results

Farheen

Ahmed

Javed

et al. 2022

Security and Communication Networks

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“…For several important results and applications, see the following literature [19][20][21][22][23][24]. Uddin et al [25] proved several fixed point results for contraction mappings in the context of orthogonal controlled FMSs. Ishtiaq et al [26] extend the results proved in [25] in a more generalized framework named orthogonal neutrosophic metric spaces.…”

Section: Introductionmentioning

confidence: 99%

“…Uddin et al [25] proved several fixed point results for contraction mappings in the context of orthogonal controlled FMSs. Ishtiaq et al [26] extend the results proved in [25] in a more generalized framework named orthogonal neutrosophic metric spaces. Recently, Uddin Disclaimer/Publisher's Note: The statements, opinions, and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s).…”

Section: Introductionmentioning

confidence: 99%

On Orthogonal Fuzzy Iterative Mappings with Applications to Volterra Type Integral Equations and Fractional Differential Equations

Ishtiaq¹,

Jahangeer²,

Kattan³

et al. 2023

Preprint

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In this paper, we report orthogonal fuzzy versions of some celebrated iterative mappings. We provide various concrete conditions on the real valued functions J,S:(0,1]→(−∞,∞) for the existence of fixed-points of (J,S)-fuzzy iterative mappings. We obtain many fixed point theorems in orthogonal fuzzy metric spaces. We apply (J,S)-fuzzy version of Banach fixed point theorem to show the existence and uniqueness of the solution. We support these results with several non-trivial examples and applications to Volterra-type integral equations and fractional differential equations.

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“…[7,8,9,10,11,12,17,18]. Some other notable studies about other proposed techniques for solving integral and fuzzy integral equations such as fuzzy b-metric-like spaces for solving integral equation [19] and control fuzzy metric spaces with the help of orthogonality for solving fuzzy integral equation [20], respectively. Some novel fixed-point results of orthogonal neutrosophic metric spaces are provided in [21].…”

Section: Introductionmentioning

confidence: 99%

Novel analytical and approximate-analytical methods for solving the nonlinear fractional smoking mathematical model

Çelık¹

2022

Sigma J Eng Nat Sci - Sigma Müh Fen Bil Derg

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Smoking is globally a challenging issue that causes many fatal health problems. In this paper, a nonlinear fractional smoking mathematical model is proposed in the context of a modified form of the Caputo fractionalorder derivative. The analytical and approximate-analytical solutions are obtained for the proposed mathematical model via the fractional differential transform method (FDTM) and Laplace Adomian decomposition method (LADM). The obtained solution is provided as a rapidly convergent series. Simulation results are provided in this paper to compare the obtained solutions by FDTM, LADM, Runge Kutta (RK) method, and reduced differential transforms method (RDTM) with the exact solution of the proposed problem. By comparing both FDTM and LADM solutions, the FDTM solution is closer to the exact solution than the LADM solution. All obtained solutions have been analyzed and compared graphically to validate the effiency and applicability of all results.

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Control Fuzzy Metric Spaces via Orthogonality with an Application

Cited by 20 publications

References 9 publications

Intuitionistic Fuzzy Double Controlled Metric Spaces and Related Results

Intuitionistic Fuzzy Double Controlled Metric Spaces and Related Results

On Orthogonal Fuzzy Iterative Mappings with Applications to Volterra Type Integral Equations and Fractional Differential Equations

Novel analytical and approximate-analytical methods for solving the nonlinear fractional smoking mathematical model

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