Browsing by Author "Sarwar, Muhammad"

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Common Fixed Point Theorem via Cyclic (alpha, beta) - (psi,phi)(S)-Contraction with Applications
(MDPI, 2019) Jarad, Fahd; Abdeljawad, Thabet; Sarwar, Muhammad; Abdeljawad, Thabet; 234808
In this paper, we introduce the notion of cyclic (alpha, beta) - (psi,phi)(S)-rational-type contraction in b-metric spaces, and using this contraction, we prove common fixed point theorems. Our work generalizes many existing results in the literature. In order to highlight the usefulness of our results, applications to functional equations are given.
Existence of Unique Solution of Urysohn and Fredholm Integral Equations in Complex Double Controlled Metric Type Spaces
(2022) Jarad, Fahd; Sarwar, Muhammad; Rahmat, Gul; Jarad, Fahd; 234808
Complex Urysohn integral equations and complex Fredholm integral equation of the second kind have intensified the attention of appreciable researchers to their solution due to their comprehensive applications. This study is devoted to the existence and uniqueness of solution to these integral equations in the setting of complete complex double controlled metric spaces via fixed point theory. For this motive, a fixed point result together with a numerical example for the convergence behavior of operator to the fixed point is analyzed in the context of the quoted metric spaces.
Fixed Point Theorems for Multi-Valued Contractions in b-Metric Spaces With Applications to Fractional Differential and Integral Equations
(IEEE-INST Electrical Electronics Engineers INC, 2019) Abdeljawad, Thabet; Jarad, Fahd; Jarad, Fahd; Sarwar, Muhammad; 234808
The aim of this manuscript is to establish common fixed points results for multi-valued mappings via generalized rational type contractions in complete b-metric spaces. Using the derived results, existence of solutions to certain integral equations and fractional differential equations in the frame of Caputo fractional derivative are studied. Examples are provided for the authenticity of the presented work.
Generalized Darbo-Type F -Contraction and F -Expansion and Its Applications to a Nonlinear Fractional-Order Differential Equation
(2020) Abdeljawad, Thabet; Jarad, Fahd; Abdeljawad, Thabet; Jarad, Fahd; 234808
In this work, we introduce various Darbo-type F£-contractions, and utilizing these contractions, we present some fixed point theorems. Moreover, we introduce a Darbo-type F£-expanding mapping and prove fixed point theorems under the Darbo-type F£-expanding mapping. Employing our results, we check the existence of a solution to the nonlinear fractional-order differential equation under the integral type boundary conditions. For its validity, an appropriate example is given. © 2020 Mian Bahadur Zada et al.
n-Tupled Common Fixed Point Result in Fuzzy b-Metric Spaces
(2022) Jarad, Fahd; Sarwar, Muhammad; Jarad, Fahd; 234808
Qualitative analysis of implicit Dirichlet boundary value problem for Caputo-Fabrizio fractional differential equations
(2020) Abdeljawad, Thabet; Jarad, Fahd; Shah, Kamal; Abdeljawad, Thabet; Jarad, Fahd; 234808
This article studies a class of implicit fractional differential equations involving a Caputo-Fabrizio fractional derivative under Dirichlet boundary conditions (DBCs). Using classical fixed-point theory techniques due to Banch's and Krasnoselskii, a qualitative analysis of the concerned problem for the existence of solutions is established. Furthermore, some results about the stability of the Ulam type are also studied for the proposed problem. Some pertinent examples are given to justify the results. Copyright © 2020 Rozi Gul et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Some Coincidence and Common Fixed-Point Results on Cone b(2)-Metric Spaces over Banach Algebras with Applications to the Infinite System of Integral Equations
(2021) Jarad, Fahd; Sarwar, Muhammad; Filali, Doaa; Jarad, Fahd; 234808
In this article, common fixed-point theorems for self-mappings under different types of generalized contractions in the context of the cone b(2)-metric space over the Banach algebra are discussed. The existence results obtained strengthen the ones mentioned previously in the literature. An example and an application to the infinite system of integral equations are also presented to validate the main results.