arXiv subjects

Tanzeela Kanwal

Publications and source records attributed to Tanzeela Kanwal.

4 recordsLinked to original sources

arXiv2024

Dynamics of a Model of Polluted Lakes via Fractal-Fractional Operators with Two Different Numerical Algorithms

We employ Mittag-Leffler type kernels to solve a system of fractional differential equations using fractal-fractional (FF) operators with two fractal and fractional orders. Using the notion of FF-derivatives with nonsingular and nonlocal fading memory, a model of three polluted lakes with one source of pollution is investigated. The properties of a non-decreasing and compact mapping are used in order to prove the existence of a solution for the FF-model of polluted lake system. For this purpose, the Leray-Schauder theorem is used. After exploring stability requirements in four versions, the proposed model of polluted lakes system is then simulated using two new numerical techniques based on Adams-Bashforth and Newton polynomials methods. The effect of fractal-fractional differentiation is illustrated numerically. Moreover, the effect of the FF-derivatives is shown under three specific input models of the pollutant: linear, exponentially decaying, and periodic.

math.DS↗

arXiv2018

Weak partial $b$-metric space and Nadler's theorem

We study the notions of weak partial $b$-metric space and weak partial Hausdorff $b$-metric space. Moreover, we intend to generalize Nadler's theorem in weak partial $b$-metric space by using weak partial Hausdorff $b$-metric spaces. A non-trivial example to show the validity of our result is given.

math.GN↗

arXiv2018

Gerghaty type results via simulation and $\mathcal{C}$-class functions with application

In this paper we study the notion of Gerghaty type contractive mapping via simulation function along with $\mathcal{C}$-class functions and prove the existence of several fixed point results in ordinary and partially ordered metric spaces. An example is given to show the validity of our results given herein. Moreover, existence of solution of two-point boundary value second order nonlinear differential equation is obtain.

math.FA↗

arXiv2018

Best proximity point results for almost contraction and application to nonlinear differential equation

Brinde [Approximating fixed points of weak contractions using the Picard itration, Nonlinear Anal. Forum 9 (2004), 43-53] introduced almost contraction mappings and proved Banach contraction principle for such mappings. The aim of this paper is to introduce the notion of multivalued almost $Θ$- contraction mappings and present some best proximity point results for this new class of mappings. As applications, best proximity point and fixed point results for weak single valued $Θ$-contraction mappings are obtained. An example is presented to support the results presented herein. An application to a nonlinear differential equation is also provided.

math.FA↗