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The main purpose of this article is to reconsider the theory of variational iteration method and embed it with Laplace transform to construct the conjoined technique variational iteration Laplace transform method. And then, by using the proposed method we solve a class of integral equations, especially fractional order Volterra type integro‐partial‐differential equations occurring in different fields of natural and social sciences. For this, we first turn to some prelude concepts and different types of equations especially integral equations of different kinds from the literature. Then, we will present step by step the embedded technique. Next, some fractional order model integral equations will be tackled using the proposed method along with some existing techniques, like the Adomian decomposition method and successive approximations method. The efficacy and authentication of the proposed technique will be analysed with the help of the obtained results and graphical exhibitions of the particular solved examples. Finally, use of the initiated method in the future for different types of equations occurring in different fields of science will be presented. [ABSTRACT FROM AUTHOR]

New fractional operators, the COVID-19 model has been studied in this paper. By using different numerical techniques and the time fractional parameters, the mechanical characteristics of the fractional order model are identified. The uniqueness and existence have been established. The model's Ulam-Hyers stability analysis has been found. In order to justify the theoretical results, numerical simulations are carried out for the presented method in the range of fractional order to show the implications of fractional and fractal orders. We applied very effective numerical techniques to obtain the solutions of the model and simulations. Also, we present conditions of existence for a solution to the proposed epidemic model and to calculate the reproduction number in certain state conditions of the analyzed dynamic system. COVID-19 fractional order model for the case of Wuhan, China, is offered for analysis with simulations in order to determine the possible efficacy of Coronavirus disease transmission in the Community. For this reason, we employed the COVID-19 fractal fractional derivative model in the example of Wuhan, China, with the given beginning conditions. In conclusion, again the mathematical models with fractional operators can facilitate the improvement of decision-making for measures to be taken in the management of an epidemic situation. [ABSTRACT FROM AUTHOR]

This paper contains several novel definitions including neutrosophic E β metric space, neutrosophic quasi- S β -metric space, neutrosophic pseudo- S β -metric space, neutrosophic quasi- E -metric space and neutrosophic pseudo- E β -metric space. Further, we present some generalized fixed point results with non-trivial examples and the decomposition theorem in the setting of the neutrosophic pseudo- E β -metric space. Moreover, by using the main result, we examine the existence and uniqueness of the solution to an integral equation, a system of linear equations, and nonlinear fractional differential equations. [ABSTRACT FROM AUTHOR]

The advent of Blockchain and its subsequent application in creating Bitcoin has changed the world of finance. The peer-to-peer Blockchain networks, lack a third-party intermediary authority to regulate the transactions, making it vulnerable to various forms of stings. One of the most proliferate uses of crypto transactions is for the ransom payment made by victims of ransomware attacks. Owing to the varied nature of the ransomware attacks, coupled with the decentralized nature of Blockchain, tracking and guarding against such attacks is still a challenge. One way to prevent ransomware attackers from easily benefitting from such crypto transactions is to identify them and avert any payment to those attackers. In this paper, the impact of three ensemble classification algorithms – Random Forest, XGBoost and Balanced Bagging are studied to correctly classify ransomware payments from existing Bitcoin transaction data, to identify the attackers’ addresses and possibly suspend them from taking part in any transactions. The outcomes of the three algorithms are compared with each other based on various indicators. From the experimental results, it could be concluded that Balanced Bagging Classifier demonstrated better performance with an accuracy of 98.41%. [ABSTRACT FROM AUTHOR]

This comprehensive investigation explores the application and significance of q-differential calculus in the realm of vector functions of several variables, addressing critical aspects such as q-Rolle’s theorem, the q-Mean-value theorem, and q-chain rule for vector functions. Additionally, we investigate the q-gradient, q-Jacobian, and q-Hessian operators, elucidating their roles in quantifying rates of change, determining directional derivatives, and characterizing critical points of multivariate functions. Furthermore, this research provides a rigorous treatment of Multivariate and Bivariate Taylor theorems in the context of q-differential calculus, presenting analytical expansions of functions around specific points and showcasing their utility in approximating functions in higher dimensions. The q-Maximum and Minimum are demonstrated and discussed as well. [ABSTRACT FROM AUTHOR]

In this article, we will solve optimization problems from the financial and economic field with constants, infinite-horizon iterative techniques and elements from fixed point theory. We will resort to C' iric' contractions in Banach space and the main result consists of the existence of a fixed point to solve an important class of infinite-horizon iterative schemes for optimization problems with state constraints for which the value function is merely lower semi-continuous. The developed tools allowed us to solve the stationary infinite-horizon optimization problems, especially for the maximization of the utility of households. We present some fixed point results that are fundamental for the development of our contributions: Notably, existence, monotonicity, attainability and results in the C' iric' contribution. We show the convergence in norm with probability for an iterative procedure defined for our problem under the stated assumptions. By using the C' iric' operator and the Reich-Rus type F-contraction, we prove the existence of the results of the optional cost function of an infinite horizon problem in a complete metric space. For a particular case, we realize a numerical simulation in C++. The conclusions are that the convergence, the existence and the uniqueness results of an optimal cost function of an infinite horizon problem in a Banach space can be treated by resorting to the C' iric' operator. [ABSTRACT FROM AUTHOR]

This article explored a specific variant of the overlapping generation model using a nonlinear Fredholm integral equation. We considered assumptions related to the Ć irić operator, offering a new perspective compared to existing research. To solve the equation, we employed the Galerkin method, which approximates it as a finite system of equations. By combining these approaches, we conducted a comprehensive analysis of the model, providing insights into its dynamics and potential applications. [ABSTRACT FROM AUTHOR]

In this manuscript, we present several types of interpolative proximal contraction mappings including Reich–Rus–Ciric-type interpolative-type contractions and Kannan-type interpolative-type contractions in the setting of bipolar metric spaces. Further, taking into account the aforementioned mappings, we prove best proximity point results. These results are an extension and generalization of existing ones in the literature. Furthermore, we provide several nontrivial examples, an application to find the solution of an integral equation, and a nonlinear fractional differential equation to show the validity of the main results. [ABSTRACT FROM AUTHOR]

This manuscript contains several new notions including intuitionistic fuzzy  N b  metric space, intuitionistic fuzzy quasi- S b -metric space, intuitionistic fuzzy pseudo- S b -metric space, intuitionistic fuzzy quasi- N -metric space and intuitionistic fuzzy pseudo  N b  fuzzy metric space. We prove decomposition theorem and fixed-point results in the setting of intuitionistic fuzzy pseudo  N b  fuzzy metric space. Further, we provide several non-trivial examples to show the validity of introduced notions and results. At the end, we solve an integral equation, system of linear equations and nonlinear fractional differential equations as applications. [ABSTRACT FROM AUTHOR]

In this article, we use the Picard-Thakur hybrid iterative scheme to approximate the fixed points of generalized α-nonexpansive mappings. For generalized α-nonexpansive mappings in hyperbolic spaces, we show several weak and strong convergence results. It is proved numerically and graphically that the Picard-Thakur hybrid iterative scheme converges more faster than other well-known hybrid iterative methods for generalized α-nonexpansive mappings. We also present an application to Fredholm integral equation. [ABSTRACT FROM AUTHOR]

The objective of this paper is to generalize and improve some results in fixed point theorems in both complete metric space and Menger space. These results are generalizations of the analogous ones recently proved by Khojasteh [5], Demma [1], Yildirim [13], where we establish a dynamic information about their other fixed points if there exist i.e the distance between two fixed point in case of metric space and their equivalent in probabilistic metric space. Some illustrative examples are furnished, which demonstrate the validity of the hypotheses. As an application to our main result, we derive a uniqueness fixed point theorem for a selfmapping under strong conditions. [ABSTRACT FROM AUTHOR]