Recently, different extensions of the fractional derivative operator are found in many research papers. The main aim of this paper is to establish an extension of the extended Caputo fractional derivative operator. The extension of an extended fractional derivative of some elementary functions derives by considering an extension of beta function which includes the Mittag-Leffler function in the kernel. Further, an extended fractional derivative of some familiar special functions, the Mellin transforms of newly defined Caputo fractional derivative operator and the generating relations for extension of extended hypergeometric functions also presented in this study.

The main objective of this present paper is to introduce further extension of extended Caputo fractional derivative operator and establish the extension of an extended fractional derivative of some known elementary functions. Also, we investigate the extended fractional derivative of some familiar special functions, the Mellin transforms of newly defined Caputo fractional derivative operator and generating relations for extension of extended hypergeometric functions.

Due to the ongoing global warming on the Earth, permafrost degradation has been extensively taking place, which poses a substantial threat to civil and industrial facilities and infrastructure elements, as well as to the utilization of natural resources in the Arctic and high-latitude regions. In order to prevent the negative consequences of permafrost thawing under the foundations of constructions, various geophysical techniques for monitoring permafrost have been proposed and applied so far: temperature, electrical, seismic and many others. At the same time, non-stationary electromagnetic methods seem to have significant potential and a number of important practical advantages. We propose a cross-borehole exploration system for the highest localization of target objects in the cryolithozone. A novel mathematical apparatus for three-dimensional modeling of transient electromagnetic (TEM) signals by the vector finite element method has been developed. The original combination of the latter, the Sumudu integral transform and artificial neural networks makes it possible to examine spatially heterogeneous objects of the cryolithozone with a high contrast of geoelectric parameters, significantly reducing computational costs. We have studied the sensitivity of the TEM signals to the boundary between thawed and frozen rocks depending on the inter-borehole distance and spatial orientations of the transmitters and receivers. Numerical simulation results of the TEM monitoring of industrial facilities located on permafrost are considered. The formation of a talik has been shown to significantly manifest itself in the measured electromagnetic responses, which enables timely prevention of industrial disasters and environmental catastrophes.

In recent years, computer-aided analysis techniques have emerged as valuable tools in assisting dermatologists by providing objective and efficient analysis of skin cancer images. This paper utilizes the combination of the Contourlet Transform (CT) and Local Binary Pattern (LBP) techniques for accurately recognizing borders, contrast changes, and shapes of skin cancer images. These results often contain many features, leading to high computational costs and potential over-fitting issues. Hence, we applied Particle Swarm Optimization (PSO) to select the most informative and discriminating features, reducing the dimensionality while retaining important information for accurate classification. After reducing the feature set with PSO, we applied these sets to Machine learning classification algorithms: Support Vector Machine (SVM), Random Forest (RF), and Neural Networks (NN). The results show that SVM has the lowest time complexity of 0.0458 seconds, followed by the Neural Network at 0.08730 seconds, and the Random Forest model has the highest time complexity of 0.1622 seconds. The SVM and Neural Network models are faster to train than the Random Forest model, making them more suitable for real-time or latency-sensitive applications. We also compared our proposed model with the state-of-the-art models and obtained the accuracy of 86.9%, which is the highest among the models.

Document deskewing is a fundamental problem in document image processing. While existing methods have limitations, such as Hough Line Transformation that can deskew images upside down, and Deep Learning models that require huge amounts of human labour and computational resources and still fail to deskew while taking care of orientation, OCR-based methods also struggle to read text when it is tilted. In this paper, we propose a novel, simple, cost-effective deep learning method for fixing the skew and orientation of documents. Our approach reduces the search space for the machine learning model to predict whether an image is upside down or not, avoiding the huge search space of predicting an angle between 0 and 360. We finetuned a MobileNetV2 model, which was pre-trained on imagenet, using only 200 images and achieve good results. This method is useful for automation-based tasks, such as data extraction using OCR technology, and can greatly reduce manual labour.

This paper presents the methodology to detect and identify the type of fault that occurs in shunt connected static synchronous compensator (STATCOM) transmission line using a combination of Discrete Wavelet Transform (DWT) and Naive Bayes classifier. To study this, the network model is designed using Mat-lab/Simulink. The different faults such as Line to Ground (LG), Line to Line (LL), Double Line to Ground (LLG) and three-phase (LLLG) fault are applied at different zones of system with and without STATCOM considering the effect of varying fault resistance. The three-phase fault current waveforms obtained are decomposed into several levels using daubechies mother wavelet of db4 to extract the features such as standard deviation and Energy values. The extracted features are used to train the classifiers such as Multi-Layer Perceptron Neural Network (MLP), Bayes and Naive Bayes (NB) classifier to classify the type of fault that occurs in the system. The results reveal that the proposed NB classifier outperforms in terms of accuracy rate, misclassification rate, kappa statistics, mean absolute error (MAE), root mean square error (RMSE), relative absolute error (RAE) and root-relative square error (RRSE) than MLP and Bayes classifier.

The main objective of this paper is to introduce k-fractional derivative operator by using the definition of k-beta function. We establish some results related to the newly defined fractional operator such as Mellin transform and relations to k-hypergeometric and k-Appell's functions. Also, we investigate the k-fractional derivative of k-Mittag-Leffler and Wright hypergeometric functions.

In this paper, we introduce a new formulation based on Floquet (Fourier) spectral analysis combined with a spectral modulation technique (and its spatial form) to study strongly coupled sublattices predefined in the infinite and large finite extent of almost periodic antenna arrays (e.g metasurfaces). This analysis is very relevant for dense massive MIMO, intelligent surfaces, 5G, and 6G applications (used for very small areas with a large number of elements such as millimeter and terahertz waves applications). The numerical method that is adopted to model the structure is the method of moments simplified by equivalent circuits MoM GEC. Other numerical methods (as the ASM array scanning method and windowing Fourier method) used this analysis in their kernel that to treat periodic and pseudo-periodic (or quasi-periodic) arrays.

This article deals with the conformable double Laplace transforms and their some properties with examples and also the existence Condition for the conformable double Laplace transform is studied. Finally, in order to obtain the solution of nonlinear fractional problems, we present a modified conformable double Laplace that we call conformable double Laplace decomposition methods (CDLDM). Then, we apply it to solve, Regular and singular conformable fractional coupled burgers equation illustrate the effectiveness of our method some examples are given.

The radar sensor described realizes healthcare monitoring capable of detecting subject chest-wall movement caused by cardiopulmonary activities, and wirelessly estimating the respiration and heartbeat rates of the subject without attaching any devices to the body. Conventional single-tone Doppler radar can only capture Doppler signatures because of a lack of bandwidth information with noncontact sensors. In contrast, we take full advantage of impulse radio ultra-wideband (IR-UWB) radar to achieve low power consumption and convenient portability, with a flexible detection range and desirable accuracy. A noise reduction method based on improved ensemble empirical mode decomposition (EEMD) and a vital sign separation method based on the continuous-wavelet transform (CWT) are proposed jointly to improve the signal-to-noise ratio (SNR) in order to acquire accurate respiration and heartbeat rates. Experimental results illustrate that respiration and heartbeat signals can be extracted accurately under different conditions. This noncontact healthcare sensor system proves the commercial feasibility and considerable accessibility of using compact IR-UWB radar for emerging biomedical applications.

We shall discuss three methods of inverse Laplace transforms. A Sinc-Thiele approxi- mation, a pure Sinc, and a Sinc-Gaussian based method. The two last Sinc related methods are exact methods of inverse Laplace transforms which allow us a numerical approximation using Sinc methods. The inverse Laplace transform converges exponentially and does not use Bromwich contours for computations. We apply the three methods to Mittag-Leffler functions incorporating one, two, and three parameters. The three parameter Mittag-Leffler function represents Prabhakar’s function. The exact Sinc methods are used to solve fractional differential equations of constant and variable differentiation order.

Compressive sensing (CS) is a technique that allows a signal vector to be reconstructed with a number of linear measurements far fewer than its size. In this study, optical hybrid cryptography with simultaneous compressive sensing based on orthogonal matching pursuit (OMP) is proposed as an alternative solution to the two important problems in communications, namely, effective / efficient / signal processing and secure encryption/decrypton. The whole system is able to both compress and encrypt data with attack immunity.

There are currently around 78 Nuclear Power Plants (NPP) in the world based on Boiling Water Reactors (BWR). The current parameter to assess BWR instability issues is the linear Decay Ratio (DR). However, it is well known that BWRs are complex non-linear dynamical systems that may even exhibit chaotic dynamics that normally preclude the use of the DR when the BWR is working at a specific operating point during instability. In this work a novel methodology based on an adaptive Shannon Entropy estimator and on Noise Assisted Empirical Mode Decomposition variants is presented. This methodology was developed for real-time implementation of a stability monitor. This methodology was applied to a set of signals stemming from several NPPs reactors (Ringhals-Sweden, Forsmark-Sweden and Laguna Verde-Mexico) under commercial operating conditions, that experienced instabilities events, each one of a different nature

This research presents a novel Customised Load Adaptive Framework (CLAF) for fault classifica-tion in Induction Motors (IMs), utilizing the Machinery Fault Prevention Technology (MFPT) Bearing Dataset. CLAF represents a pioneering approach that extends traditional fault classification methodologies by accounting for load variations and dataset customization. Through a meticulous two-phase process, it unveils load-dependent fault subclasses that have not been readily identified in traditional approaches. Additionally, new classes are created to accommodate the dataset's unique characteristics. Phase 1 involves the exploration of load-dependent patterns in time and frequency domain features using one-way Analysis of Variance (ANOVA) ranking and validation via bagged tree classifiers. In Phase 2, CLAF is applied to identify mild, moderate, and severe load-dependent fault subclasses through optimal Continuous Wavelet Transform (CWT) selection through Wavelet Singular Entropy (WSE) and CWT energy analysis. The results are compelling, with a 96.3% classification accuracy achieved when employing a wide neural network to classify proposed load-dependent fault subclasses. This underscores the practical value of CLAF in en-hancing fault diagnosis in IMs and its future potential in advancing IM condition monitoring.

The main objective of this paper is to introduce a further extension of extended (p, q)-beta function by considering two Mittag-Leffler function in the kernel. We investigate various properties of this newly defined beta function such as integral representations, summation formulas and Mellin transform. We define extended beta distribution and its mean, variance and moment generating function with the help of extension of beta function. Also, we establish an extension of extended (p, q)-hypergeometric and (p, q)-confluent hypergeometric functions by using the extension of beta function. Various properties of newly defined extended hypergeometric and confluent hypergeometric functions such as integral representations, Mellin transformations, differentiation formulas, transformation and summation formulas are investigated.

This paper presents a comprehensive comparative analysis of four different computational vision algorithms for implementing an unpalleting system in a factory environment, under typical edge computing constraints. The primary objective is to automate the process of detecting and locating specific variable-shaped objects on a pallet, enabling a robotic system to accurately unstack them. The four algorithms evaluated are Pattern Matching, Scale-Invariant Feature Transform, Oriented FAST and Rotated BRIEF, and Haar cascade classifiers. Each technique is described in detail in this paper, and their implementations are outlined. Experimental results are thoroughly analyzed, assessing the algorithms’ performance based on accuracy, robustness to variability, computational speed, detection sensitivity, and resource consumption. The findings reveal the strengths and limitations of each algorithm, providing valuable insights for selecting the most appropriate technique based on the specific requirements of the unpalleting system. This research contributes to the advancement of automated object detection and localization in industrial environments, paving the way for more efficient and reliable unpalleting systems.

A new generalization of extended beta function and its various properties, integral representations and distribution are given in this paper. In addition, we establish the generalization of extended hypergeometric and con uent hypergeometric functions using the newly extended beta function. The properties these extended and con uent hypergeometric functions such as integral representations, Mellin transformations, dif- ferentiation formulas, transformation and summation formulas are also investigated.

This study presents a method for the rapid and accurate generation of two-dimensional (2D) orthomosaic maps using selected image data collected by drone-captured video. The focus is on developing a real-time method capable of creating maps more quickly than image selection. The scale-invariant feature transform (SIFT) algorithm is applied to drone images to extract features in various scale regions. For feature point matching, a matching method based on the fast library for approximate nearest neighbors (FLANN) was adopted. A comparison of the computational speed of the FLANN with that of the k-nearest neighbors (KNN) and brute force matcher during the matching process revealed FLANN's superior capability for real-time data processing. The random sample consensus (RANSAC) algorithm was employed to enhance the accuracy of the matching by removing outliers, effectively identifying and eliminating mismatches, and reinforcing the reliability of feature point matching. The combination of SIFT, FLANN, and RANSAC algorithms demonstrates the capacity to process drone-captured image data in real time, facilitating the generation of precise 2D orthomosaic maps. The proposed method was assessed and validated using imagery obtained as the drone executed curvilinear and straight flight paths, confirming its accuracy and operational efficiency concurrently with the image capture process.

Recently, Gohar et al. introduced a novel, local, and well-behaved fractional calculus. It possesses all the classical properties, and Its locality imposes simplicity and accuracy in modeling fractional order systems. In this article, we further develop the definitions and extend the classical properties of Gohar fractional calculus to address some of the open problems in Calculus. The fractional Gronwall's integral inequality, Taylor power series expansion, and Laplace transform are defined and applied to overcome some of the limitations in the classical integer-order calculus. The fractional Laplace transform is applied to solve Bernoulli-type logistic and Bertalanffy nonlinear fractional differential equations, and the criteria under which it can be applied to solve linear differential equations are investigated.

Keywords: Electrical power systems, Support vector machines, Random Forest, Machine learning, Wavelet transform, Transmission lines fault, Electrical power quality, Short circuit, Classification of faults, Localization of faults, Decision trees, Ensemble learning, K-nearest neighbors.

In this paper we discuss a problem of generalization of binomial distributed triangle, that is sequence A287326 in OEIS. The main property of A287326 that it returns a perfect cube n as sum of n-th row terms over k; 0 ≤ k ≤ n−1 or 1 ≤ k ≤ n, by means of its symmetry. In this paper we have derived a similar triangles in order to receive powers m = 5; 7 as row items sum and generalized obtained results in order to receive every odd-powered monomial n^2m+1; m ≥ 0 as sum of row terms of corresponding triangle. In other words, in this manuscript are found and discussed the polynomials D_m(n,k) and U_m(n,k), such that, when being summed up over k in some range with respect to m and n returns the monomial n^2m+1.