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We employ Mittag-Leffler type kernels to solve a system of fractional differential equations using fractal-fractional (FF) operators with two fractal and fractional orders. Using the notion of FF-derivatives with nonsingular and nonlocal fading memory, a model of three polluted lakes with one source of pollution is investigated. The properties of a non-decreasing and compact mapping are used in order to prove the existence of a solution for the FF-model of polluted lake system. For this purpose, the Leray-Schauder theorem is used. After exploring stability requirements in four versions, the proposed model of polluted lakes system is then simulated using two new numerical techniques based on Adams-Bashforth and Newton polynomials methods. The effect of fractal-fractional differentiation is illustrated numerically. Moreover, the effect of the FF-derivatives is shown under three specific input models of the pollutant: linear, exponentially decaying, and periodic., Comment: This is a preprint of a paper whose final and definite form is published Open Access in 'Chaos Solitons Fractals' at [https://doi.org/10.1016/j.chaos.2024.114653]

We consider a system to optimize duration of traffic signals using multi-agent deep reinforcement learning and Vehicle-to-Everything (V2X) communication. This system aims at analyzing independent and shared rewards for multi-agents to control duration of traffic lights. A learning agent traffic light gets information along its lanes within a circular V2X coverage. The duration cycles of traffic light are modeled as Markov decision Processes. We investigate four variations of reward functions. The first two are unshared-rewards: based on waiting number, and waiting time of vehicles between two cycles of traffic light. The third and fourth functions are: shared-rewards based on waiting cars, and waiting time for all agents. Each agent has a memory for optimization through target network and prioritized experience replay. We evaluate multi-agents through the Simulation of Urban MObility (SUMO) simulator. The results prove effectiveness of the proposed system to optimize traffic signals and reduce average waiting cars to 41.5 % as compared to the traditional periodic traffic control system., Comment: 7 Figure, Table 1

Recently, the advancement in industrial automation and high-speed printing has raised numerous challenges related to the printing quality inspection of final products. This paper proposes a machine vision based technique to assess the printing quality of text on industrial objects. The assessment is based on three quality defects such as text misalignment, varying printing shades, and misprinted text. The proposed scheme performs the quality inspection through stochastic assessment technique based on the second-order statistics of printing. First: the text-containing area on printed product is identified through image processing techniques. Second: the alignment testing of the identified text-containing area is performed. Third: optical character recognition is performed to divide the text into different small boxes and only the intensity value of each text-containing box is taken as a random variable and second-order statistics are estimated to determine the varying printing defects in the text under one, two and three sigma thresholds. Fourth: the K-Nearest Neighbors based supervised machine learning is performed to provide the stochastic process for misprinted text detection. Finally, the technique is deployed on an industrial image for the printing quality assessment with varying values of n and m. The results have shown that the proposed SAML-QC technique can perform real-time automated inspection for industrial printing., Comment: 7 Pages, 10 figures, 6 Tables

We study the notions of weak partial $b$-metric space and weak partial Hausdorff $b$-metric space. Moreover, we intend to generalize Nadler's theorem in weak partial $b$-metric space by using weak partial Hausdorff $b$-metric spaces. A non-trivial example to show the validity of our result is given.

In this paper we study the notion of Gerghaty type contractive mapping via simulation function along with $\mathcal{C}$-class functions and prove the existence of several fixed point results in ordinary and partially ordered metric spaces. An example is given to show the validity of our results given herein. Moreover, existence of solution of two-point boundary value second order nonlinear differential equation is obtain., Comment: arXiv admin note: text overlap with arXiv:1810.09969

The aim of this paper is to introduce the notion of a Suzuki-Gerghaty type contractive mapping via simulation function along with $\mathcal{C}$-class functions and prove the existence of fixed point result. An example is given to show the validity of our results given herein. Moreover, we prove the existence of solution of nonlinear Hammerstein integral equation.

Brinde [Approximating fixed points of weak contractions using the Picard itration, Nonlinear Anal. Forum 9 (2004), 43-53] introduced almost contraction mappings and proved Banach contraction principle for such mappings. The aim of this paper is to introduce the notion of multivalued almost $\Theta$- contraction mappings and present some best proximity point results for this new class of mappings. As applications, best proximity point and fixed point results for weak single valued $\Theta$-contraction mappings are obtained. An example is presented to support the results presented herein. An application to a nonlinear differential equation is also provided.