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In the present work, we introduce a notion of generalized contractive conditions involving rational terms for four mappings in the setting of complex valued metric spaces and develop common fixed point results for two pairs of weakly compatible mappings satisfying introduced contractive condition. A common fixed point theorem for four finite families of self mappings is presented as an application of such result. The main result is applied to prove the existence and uniqueness of common solution for the system of Urysohn integral equations of the form: ... where j = 1, 2, 3, 4, a, b ∈ ℝ with a ≤ b, t ∈ [a, b], z, φj ∈ C([a, b], ℝn) and Gj: [a, b] x [a, b] x ℝn → ℝn is a given mapping for each j = 1, 2, 3, 4. [ABSTRACT FROM AUTHOR]

Recently, Choudhury and Metiya proved some fixed point theorems for weak contractions in cone metric spaces. Weak contractions are generalizations of Banach's contraction mapping, which have been studied by several authors. Here, we introduce the notion of f-weak contractions and also establish a coincidence and common fixed point result for f-weak contractions in cone metric spaces. Our result is supported by an example which includes and generalizes the results of Choudhury and Metiya's work. [ABSTRACT FROM AUTHOR]

A theory of chemical graphs is a part of mathematical chemistry concerned with the effects of connectedness in chemical graphs. Several researchers have studied the solutions of fractional differential equations using the concept of star graphs. They employed star graphs because their technique requires a central node with links to adjacent vertices but no edges between nodes. The purpose of this paper is to extend the method's range by introducing the concept of an octane graph, which is an essential organic compound having the formula C8H18. In this manner, we analyze a graph with vertices annotated by 0 or 1, which is influenced by the structure of the chemical substance octane, and formulate a fractional boundary value problem on each of the graph's edges. We use the Schaefer and Krasnoselskii fixed point theorems to investigate the existence of solutions to the presented boundary value problems in the framework of the Caputo fractional derivative. Finally, two examples are provided to highlight the importance of our results in this area of study., Competing Interests: The authors have declared that no competing interests exist.

This paper aims to suggest a time-fractional S P E P I P A I P S P H P R P model of the COVID-19 pandemic disease in the sense of the Atangana-Baleanu-Caputo operator. The proposed model consists of six compartments: susceptible, exposed, infected (asymptomatic and symptomatic), hospitalized and recovered population. We prove the existence and uniqueness of solutions to the proposed model via fixed point theory. Furthermore, a stability analysis in the context of Ulam-Hyers and the generalized Ulam-Hyers criterion is also discussed. For the approximate solution of the suggested model, we use a well-known and efficient numerical technique, namely the Toufik-Atangana numerical scheme, which validates the importance of arbitrary order derivative ϑ and our obtained theoretical results. Finally, a concise analysis of the simulation is proposed to explain the spread of the infection in society., Competing Interests: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (© 2022 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.)

We study the generalized Ulam-Hyers stability, the well-posedness, and the limit shadowing of the fixed point problem for new type of generalized contraction mapping, the so-called α-β-contraction mapping. Our results in this paper are generalized and unify several results in the literature as the result of Geraghty (1973) and the Banach contraction principle.

We extend the notion of generalized weakly contraction mappings due to Choudhury et al. (2011) to generalized α-β-weakly contraction mappings. We show with examples that our new class of mappings is a real generalization of several known classes of mappings. We also establish fixed point results for such mappings in metric spaces. Applying our new results, we obtain fixed point results on ordinary metric spaces, metric spaces endowed with an arbitrary binary relation, and metric spaces endowed with graph.