Iterative Construction of Fixed Points for Functional Equations and Fractional Differential Equations by Latif Ur Rahman, Muhammad Arshad, Sabri T. M. Thabet, Imed Kedim

“…Our results are new and generalize several comparable results in fixed point theory and applications.…”
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Some Remarks on Fixed Point Theorems for Interpolative Kannan Contraction by Youssef Errai, El Miloudi Marhrani, Mohamed Aamri

“…Our results extend and improve some results on fixed point theory in the literature. We also give some examples to illustrate the given results.…”
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New Existence Results for Nonlinear Fractional Integrodifferential Equations by Lahcen Ibnelazyz, Karim Guida, Khalid Hilal, Said Melliani

“…Some new existence and uniqueness results are proposed by using the fixed point theory. In particular, we make use of the Banach contraction mapping principle and Krasnoselskii’s fixed point theorem under some weak conditions. …”
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Sixth-Kind Chebyshev and Bernoulli Polynomial Numerical Methods for Solving Nonlinear Mixed Partial Integrodifferential Equations with Continuous Kernels by Abeer M. Al-Bugami, Mohamed A. Abdou, Amr M. S. Mahdy

“…Then, using different numerical methods, the Bernoulli polynomial method and the Chebyshev polynomials of the sixth kind, the nonlinear Fredholm integral equation has been reduced into a system of nonlinear algebraic equations. The Banach fixed-point theory is utilized in order to have a conversation about the nonlinear mixed integral equation’s solution, namely, its existence and uniqueness. …”
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Fixed Point Theorems for α,k,θ,φ-Contraction Multivalued Mappings in b-Metric Space by Youssef Errai, El Miloudi Marhrani, Mohamed Aamri

“…Our results expand and refine some of the literature’s findings in fixed point theory.…”
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New Results of Fixed-Point Theorems and Their Applications in Complete Complex Dc∗-Metric Spaces by Nassar Aiman Majid, Alaa. M. F. AL. Jumaili, Zhen Chuan Ng, See Keong Lee

“…Additionally, some implementations of common fixed-point theory on complete complex-valued Dc∗-metric spaces have been offered by applying open and closed balls. …”
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Dynamical Analysis of SIR Epidemic Model with Nonlinear Pulse Vaccination and Lifelong Immunity by Wencai Zhao, Juan Li, Xinzhu Meng

“…Firstly, by using stroboscopic map and fixed point theory of difference equations, the existence of disease-free periodic solution is discussed, and the globally asymptotical stability of disease-free periodic solution is proven by using Floquet multiplier theory and differential impulsive comparison theorem. …”
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Euler’s Numerical Method on Fractional DSEK Model under ABC Derivative by Fareeha Sami Khan, M. Khalid, Omar Bazighifan, A. El-Mesady

“…This paper gives a brief overview of the ABC fractional derivative and its attributes. Fixed point theory has been used to establish the uniqueness and existence of solutions for the fractional DSEK model. …”
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Positive Solutions for Second-Order Singular Semipositone Differential Equations Involving Stieltjes Integral Conditions by Jiqiang Jiang, Lishan Liu, Yonghong Wu

“…By means of the fixed point theory in cones, we investigate the existence of positive solutions for the following second-order singular differential equations with a negatively perturbed term: −u′′(t)=λ[f(t,u(t))−q(t)], 0<t<1, αu(0)−βu′(0)=∫01u(s)dξ(s), γu(1)+δu′(1)=∫01u(s)dη(s), where λ>0 is a parameter; f:(0,1)×(0,∞)→[0,∞) is continuous; f(t,x) may be singular at t=0, t=1, and x=0, and the perturbed term q:(0,1)→[0,+∞) is Lebesgue integrable and may have finitely many singularities in (0,1), which implies that the nonlinear term may change sign.…”
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Study of a Fractal-Fractional Smoking Models with Relapse and Harmonic Mean Type Incidence Rate by Zareen A. Khan, Mati ur Rahman, Kamal Shah

“…We derive the existence and unique results about the solution for the considered model via fixed point theory. For the stability of the considered system, Ulam-Hyers (UH) approach is used. …”
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Rational-type fixed-point theorems in b-metric spaces and their application to economic growth and market equilibrium by Khaled Aldwoah, Syed Khayyam Shah, Alaa Mustafa, Mohammed A. Almalahi, Mohammed Hassan, Amer Alsulami

“…Utilizing the idea of Wardowski (Fixed Point Theory Appl. 2012:94, 2012), novel fixed-point results are demonstrated via the iteration technique. …”
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Multivalued Fixed Point Results for Two Families of Mappings in Modular-Like Metric Spaces with Applications by Tahair Rasham, Abdullah Shoaib, Choonkil Park, Manuel de la Sen, Hassen Aydi, Jung Rye Lee

“…The aim of this research work is to find out some results in fixed point theory for a pair of families of multivalued mappings fulfilling a new type of U-contractions in modular-like metric spaces. …”
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Discontinuous differential equation for modelling the Antarctic Circumpolar Current by Michal Fečkan, Shan Li, JinRong Wang

“…By considering the piecewise vorticity function, we demonstrated the existence of solution corresponding to the discontinuous differential equation using Green's function, fixed point theory, and topological degree theory. This primarily included cases with piecewise constant vorticity, piecewise linear vorticity, and piecewise nonlinear vorticity. …”
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The Transmission Dynamics of Hepatitis B Virus via the Fractional-Order Epidemiological Model by Tahir Khan, Zi-Shan Qian, Roman Ullah, Basem Al Alwan, Gul Zaman, Qasem M. Al-Mdallal, Youssef El Khatib, Khaled Kheder

“…Once we develop the model under consideration, existence and uniqueness analysis will be discussed. We use fixed point theory for the existence and uniqueness analysis. …”
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Iterative Construction of Fixed Points for Operators Endowed with Condition E in Metric Spaces by Junaid Ahmad, Kifayat Ullah, Hüseyin Işik, Muhammad Arshad, Manuel de la Sen

“…This approach essentially provides a new setting for researchers who are working on the iterative procedures in fixed point theory and applications.…”
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A fractional mathematical model for assessing cancer risk due to smoking habits by Anil Chavada, Nimisha Pathak, Sagar R. Khirsariya

“…The existence and uniqueness of the model solution were established using Banach's fixed-point theory. For stability, we investigated the steady state points and basic reproduction number of the system. …”
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Modelling epidemiological dynamics with pseudo-recovery via fractional-order derivative operator and optimal control measures. by Samson Olaniyi, Furaha M Chuma, Ramoshweu S Lebelo, Richard C Ogbonna, Sulaimon F Abimbade

“…The well-posedness of the model is qualitatively investigated through Banach fixed point theory technique. The spread of the disease in the population is measured by analysing the basic reproduction of the model with respect to its parameters through the sensitivity analysis. …”
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Pole Allocation Applied to Two Buildings Connected by Joint Damper by Yoshiki Ikeda, Yuki Matsumoto

“…The past fixed-point theories do not provide the additional damping effect but the optimum damping coefficient of the joint damper. …”
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Artificial neural networks for stability analysis and simulation of delayed rabies spread models by Ramsha Shafqat, Ateq Alsaadi

“…The existence and uniqueness of solutions was demonstrated using fixed-point theory within the context of piecewise derivatives and integrals. …”
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A fractal–fractional order modeling approach to understanding stem cell-chemotherapy combinations for cancer by Esam Y. Salah, Bhausaheb Sontakke, Ahmed A. Hamoud, Homan. Emadifar, Atul Kumar

“…In the analytical part, we study the existence of the solution and its uniqueness, which was studied based on the fixed point theory. The equilibrium points were also studied and discussed after stem cell therapy, and the approximate solutions for the given model were obtained using the Adam Bashford method, which depends on interpolation with Lagrange polynomials. …”
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