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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]

In this paper, we introduce the b-triangular property in fuzzy b-metric space. Furthermore, we give some new fixed point results in fuzzy b-metric space for non-continuous mappings. Our results generalize and expand some results from the related literature. Two applications of our results, to solving Fredholm integral equation and in dynamic programming, are also given. [ABSTRACT FROM AUTHOR]

In this paper, the new representations of optical wave solutions to fiber Bragg gratings with cubic–quartic dispersive reflectivity having the Kerr law of nonlinear refractive index structure are retrieved with high accuracy. The residual power series technique is used to derive power series solutions to this model. The fractional derivative is taken in Caputo's sense. The residual power series technique (RPST) provides the approximate solutions in truncated series form for specified initial conditions. By using three test applications, the efficiency and validity of the employed technique are demonstrated. By considering the suitable values of parameters, the power series solutions are illustrated by sketching 2D, 3D, and contour profiles. The analysis of the obtained results reveals that the RPST is a significant addition to exploring the dynamics of sustainable and smooth optical wave propagation across long distances through optical fibers. [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]

We have developed a Jungck version of the DK iterative scheme called the Jungck–DK iterative scheme. Our analysis focuses on the convergence and stability of the Jungck–DK scheme for a pair of non-self-mappings using the more general contractive condition. We demonstrate that this iterative scheme converges faster than all other leading Jungck-type iterative schemes. To further illustrate its effectiveness, we provide an example to verify the rate of convergence and prove the data dependence result for the Jungck–DK iterative scheme. Finally, we calculate the escape criteria for generating Mandelbrot and Julia sets for polynomial functions and present visually appealing images of these sets by our modified iteration. [ABSTRACT FROM AUTHOR]

In this paper we introduce the concept of complex-valued double controlled metric like spaces. These new results generalize and extend the corresponding results about complex-valued double controlled metric type spaces. We prove some complex-valued fixed point theorems in this new complex-valued metric like spaces and, as application, we give an existence and uniqueness of the solution of a Fredholm type integral equation result. Moreover, some examples are also presented in favor of our given results. [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]

The main goal of this paper is to introduce a new scheme, known as the Aboodh homotopy integral transform method ( A HITM), for the approximate solution of wave problems in multi-dimensional orders. The Aboodh integral transform ( A IT) removes the restriction of variables in the recurrence relation, whereas the homotopy perturbation method (HPM) derives the successive iterations using the initial conditions. The convergence analysis is provided to study a wave equation with multiple dimensions. Some computational applications are considered to show the efficiency of this scheme. Graphical representation between the approximate and the exact solution predicts the high rate of convergence of this approach. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the fractal-fractional Malkus Waterwheel model in detail. We discuss the existence and uniqueness of a solution of the fractal-fractional model using the fixed point technique. We apply a very effective method to obtain the solutions of the model. We prove with numerical simulations the accuracy of the proposed method. We put in evidence the effects of the fractional order and the fractal dimension for a symmetric Malkus Waterwheel model. [ABSTRACT FROM AUTHOR]

In this study we will check the stability of the semi analytical technique, the Laplace variational iteration (LVI) scheme, which is the combination of a variational iteration technique and the Laplace transform method. Then, we will apply it to solve some non-linear fractional order partial differential equations. Since the Laplace transform cannot be applied to non-linear problems, the combination of the variational iteration technique with it will give a better and rapidly convergent sequence. Exact solutions may also exist, but we will show that the coupled technique is much better to approximate the exact solutions. The Caputo–Fabrizio fractional derivative will be used throughout the study. In addition, some possible implications of the results given here are connected with fixed point theory. [ABSTRACT FROM AUTHOR]

In this article we have introduced a metric named complex valued controlled metric type space, more generalized form of controlled metric type spaces. This concept is a new extension of the concept complex valued b-metric type space and this one is different from complex valued extended bmetric space. Using the idea of this new metric, some fixed point theorems involving Banach, Kannan and Fisher contractions type are proved. Some examples togetheran application are described to sustain our primary results. [ABSTRACT FROM AUTHOR]

This study develops a fractional model using the Caputo–Fabrizio derivative with order α for platelet-poor plasma arising in a blood coagulation system. The existence of solutions ensures that there are solutions to the considered system of equations. Approximate solutions to the recommended model are presented by selecting different numbers of fractional orders and initial conditions (ICs). For each case, graphs of solutions are supplied through different dimensions. [ABSTRACT FROM AUTHOR]

In this article, the authors introduced the concept of graphical fuzzy metric spaces which is a generalization of fuzzy metric spaces with the help of a relation. The authors discussed some topological structure, convergence criteria, and proved a Banach fixed-point result in graphical fuzzy metric space. As an application of obtained results, the authors find a solution of an integral equation and nonlinear fractional differential equations in the context of graphical fuzzy metric spaces. The authors provided some examples to illustrate the obtained results herein. [ABSTRACT FROM AUTHOR]

In this manuscript, some tripled fixed point results are presented in the framework of complete metric spaces. Furthermore, Wardowski's contraction was mainly applied to discuss some theoretical results with and without a directed graph under suitable assertions. Moreover, some consequences and supportive examples are derived to strengthen the main results. In the last part of the paper, the obtained theoretical results are used to find a unique solution to a system of functional and integral equations. [ABSTRACT FROM AUTHOR]

In this work, we combined two techniques, the variational iteration technique and the Laplace transform method, in order to solve some nonlinear-time fractional partial differential equations. Although the exact solutions may exist, we introduced the technique VITM that approximates the solutions that are difficult to find. Even a single iteration best approximates the exact solutions. The fractional derivatives being used are in the Caputo-Fabrizio sense. The reliability and efficiency of this newly introduced method is discussed in details from its numerical results and their graphical approximations. Moreover, possible consequences of these results as an application of fixed-point theorem are placed before the experts as an open problem. [ABSTRACT FROM AUTHOR]

In this paper, we introduce fixed point theorem for a general contractive condition in complex valued metric spaces. Also, some important corollaries under this contractive condition are obtained. As an application, we find a unique solution for Urysohn integral equations and some illustrative examples are given to support our obtaining results. Our results extend and generalize the results of Azam et al. [2] and some other known results in the literature. [ABSTRACT FROM AUTHOR]

The Rovinari Thermal Power Plant is one of the electricity suppliers of Oltenia (together with Turceni Thermal Power Plant, Craiova Thermal Power Plant) covering one third of the national electricity production. The aim of this paper is to determine practically, by drilling, the physical and mechanical characteristics of the soil in the area of Rovinari Thermal Power Plant. The paper is intended to be an introduction to a broader study on the influence of mining lignite quarries in the Rovinari mining basin on the stability of the buildings in the Rovinari thermal power plant and its coal and slag-ash deposits. This stability depends on the safe functioning of the thermal power plant throughout its lifetime. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study the data dependence for the fixed point set of a multivalued weakly contractive operator with respect to a w-distance in the sense of T. Suzuki and W. Takahashi. We also give a fixed point result for a multivalued weakly '-contraction on a metric space endowed with a w-distance. [ABSTRACT FROM AUTHOR]

In this paper we present some xed point results for multivalued operators, which extend the ones given by A.I. Perov and A.V. Kribenko, as well as some recent contributions due to A. Bucur, L. Guran and A. Petrşusel. [ABSTRACT FROM AUTHOR]

In this article, we apply one fixed point theorem in the setting of b-metric-like spaces to prove the existence of solutions for one type of Caputo fractional differential equation as well as the existence of solutions for one integral equation created in mechanical engineering. [ABSTRACT FROM AUTHOR]

For modeling of complex systems, in signal processing, and the explorations of nonlinear dynamics and memory effects, the utilization of noninteger-order dynamics provides adaptable control over oscillation patterns and frequencies. Moreover, various waveforms result in unique sonic qualities. By manipulation of these waveforms, musicians and sound designers have the capacity to craft a wide spectrum of auditory experiences, ranging from basic tones to intricate sound scape. This paper is about study of such vibrating systems using the noninteger-order derivative operator approach. In particular, we will discuss fractional relaxation oscillator and Scott-Blair oscillator employing constant proportional Caputo fractional derivative operator. Laplace transform method and Tzou’s numerical inversion algorithm are utilized to solve these vibrating models with respective initial conditions. A thorough graphical analysis is done to discuss the control of noninteger-order parameters and the parameters involved in the definition of fractional derivative operator. Finally, useful conclusions are recorded to highlight the behavior of oscillators and influence of noninteger-order parameters, the parameters involved in the definition of fractional derivative operator and system parameters that are helpful in controlling over oscillation pattern, frequencies and shape of vibrations produced by the vibrating systems. [ABSTRACT FROM AUTHOR]

This manuscript is focused on the role of convexity of the modular, and some fixed point results for contractive correspondence and single-valued mappings are presented. Further, we prove Nadler's Theorem and some fixed point results on orthogonal modular spaces. We present an application to a particular form of integral inclusion to support our proposed version of Nadler's theorem. [ABSTRACT FROM AUTHOR]

In this paper we give some common fixed point theorems for Ćirić type operators in complex valued b-metric spaces. Also, some corollaries under this contraction condition are obtained. Our results extend and generalize the results of Hammad et al. In the second part of the paper, in order to strengthen our main results, an illustrative example and some applications are given. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to prove fixed point theorems for cyclic-type operators in extended b-metric spaces. The well-posedness of the fixed point problem and limit shadowing property are also discussed. Some examples are given in order to support our results, and the last part of the paper considers some applications of the main results. The first part of this section is devoted to the study of the existence of a solution to the boundary value problem. In the second part of this section, we study the existence of solutions to fractional boundary value problems with integral-type boundary conditions in the frame of some Caputo-type fractional operators. [ABSTRACT FROM AUTHOR]

In this paper, we give an affirmative answer to an open question posed recently by Mlaiki et al. As a consequence of our results, we get some known results in the literature. We also give an application of our results to the existence of a solution of nonlinear fractional differential equations. [ABSTRACT FROM AUTHOR]

The aim of this paper is to give some fixed point results in generalized metric spaces in Perov's sense. The generalized metric considered here is the w-distance with a symmetry condition. The operators satisfy a contractive weakly condition of Hardy–Rogers type. The second part of the paper is devoted to the study of the data dependence, the well-posedness, and the Ulam–Hyers stability of the fixed point problem. An example is also given to sustain the presented results. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to present some new fixed point results in the generalized metric spaces of Perov's sense under a contractive condition of Hardy–Rogers type. The data dependence of the fixed point set, the well-posedness of the fixed point problem and the Ulam–Hyers stability are also studied. [ABSTRACT FROM AUTHOR]