Brock's approaching zero method improved as approaching fixed point frequency to solve optimum damping ratio of dynamic vibration absorber in machine tools and experimental confirm... by Hongliang Tian, Xixiao Liang, Xuan Du

“…Many computational parameters of the main vibration system were attained. The fixed point theory essentially computes the extreme large value, not the maximum value. …”
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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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On the existence of solutions to fractional differential equations involving Caputo q-derivative in Banach spaces by Isra Al-Shbeil, Houari Bouzid, Benali Abdelkader, Alina Alp Lupas, Mohammad Esmael Samei, Reem K. Alhefthi

“…We analyze the existence and uniqueness of solutions to the multi-point nonlinear BVPs base on fixed point theory, including fixed point theorem of Banach, Leray-nonlinear Schauder's alternative, and Leray-degree Schauder's theory. …”
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Fractional and stochastic modeling of breast cancer progression with real data validation. by Khaled Aldwoah, Hanen Louati, Nedal Eljaneid, Tariq Aljaaidi, Faez Alqarni, AbdelAziz Elsayed

“…Theoretical analysis, employing fixed-point theory for the fractional-order phases and Ito calculus for the stochastic phase, establishes the existence and uniqueness of solutions. …”
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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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Qualitative results and numerical approximations of the $ (k, \psi) $-Caputo proportional fractional differential equations and applications to blood alcohol levels model by Weerawat Sudsutad, Chatthai Thaiprayoon, Aphirak Aphithana, Jutarat Kongson, Weerapan Sae-dan

“…The existence and uniqueness results were proven utilizing the fixed point theory of Banach's and Leray-Schauder's types. …”
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Numerical Algorithm for Coupled Fixed Points in Normed Spaces with Applications to Fractional Differential Equations and Economics by Lifang Guo, Salha Alshaikey, Abeer Alshejari, Muhammad Din, Umar Ishtiaq

“…This class of operators addresses mappings with discontinuities or non-self mappings, enhancing the applicability of fixed-point theory to more complex problems. This class of operators expands on existing cyclic contractions, including interpolative Kannan mappings, interpolative Reich–Rus–Ćirić contractions, and other known contractions in the literature. …”
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Applying fractional calculus to malware spread: A fractal-based approach to threat analysis. by Nausheen Razi, Muhammad Bilal Riaz, Ambreen Bano, Tayyab Kamran, Umar Ishtiaq, Anum Shafiq

“…In this paper, theoretical analysis is performed by concepts of fixed point theory. Existence, uniqueness and stability conditions are investigated for FF model. …”
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Bifurcation and controller design in a 3D delayed predator-prey model by Jinting Lin, Changjin Xu, Yiya Xu, Yingyan Zhao, Yicheng Pang, Zixin Liu, Jianwei Shen

“…Based on previous studies, this article construct a novel delayed predator-prey model. By utilizing fixed point theory, inequality methods, and appropriate functions, this article examined the desirable properties of the solutions of the constructed delayed predator-prey system, including existence and uniqueness, boundedness, and non-negativity. …”
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A sustainable method for analyzing and studying the fractional-order panic spreading caused by the COVID-19 pandemic by Muhammad Farman, Evern Hincal, Parvaiz Ahmad Naik, Ali Hasan, Aceng Sambas, Kottakkaran Sooppy Nisar

“…Unique solution and Picards stability of iterative scheme verified by using the fixed point theory concept. To discover the solution of the fractional order system and evaluate the effect of fractional parameters, an advanced numerical approach is applied. …”
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Fractional-order PID feedback synthesis controller including some external influences on insulin and glucose monitoring by Kottakkaran Sooppy Nisar, Muhammad Farman, Khadija Jamil, Saba Jamil, Evren Hincal

“…Additionally, a new theorem is proven using fixed-point theory, confirming the existence and uniqueness of the fractional-order model. …”
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