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In recent years, various results of the special matrix functions have been established in many papers. In the present paper, we have developed certain properties involving generalised hypergeometric matrix functions, such as, integral representations and reduction formulae. Also, open problems concerning the generalised hypergeometric matrix functions are stated.

In this paper we propose two novel deep convolutional network architectures, CovidResNet and CovidDenseNet, to diagnose COVID-19 based on CT images. The models enable transfer learning between different architectures, which might significantly boost the diagnostic performance. Whereas novel architectures usually suffer from the lack of pretrained weights, our proposed models can be partly initialized with larger baseline models like ResNet50 and DenseNet121, which is attractive because of the abundance of public repositories. The architectures are utilized in a first experimental study on the SARS-CoV-2 CT-scan dataset, which contains 4173 CT images for 210 subjects structured in a subject-wise manner into three different classes. The models differentiate between COVID-19, non-COVID-19 viral pneumonia, and healthy samples. We also investigate their performance under three binary classification scenarios where we distinguish COVID-19 from healthy, COVID-19 from non-COVID-19 viral pneumonia, and non-COVID-19 from healthy, respectively. Our proposed models achieve up to 93.87% accuracy, 99.13% precision, 92.49% sensitivity, 97.73% specificity, 95.70% F1-score, and 96.80% AUC score for binary classification, and up to 83.89% accuracy, 80.36% precision, 82.04% sensitivity, 92.07% specificity, 81.05% F1-score, and 94.20% AUC score for the three-class classification tasks. We also validated our models on the COVID19-CT dataset to differentiate COVID-19 and other non-COVID-19 viral infections, and our CovidDenseNet model achieved the best performance with 81.77% accuracy, 79.05% precision, 84.69% sensitivity, 79.05% specificity, 81.77% F1-score, and 87.50% AUC score. The experimental results reveal the effectiveness of the proposed networks in automated COVID-19 detection where they outperform standard models on the considered datasets while being more efficient.

MSC Classification: 30G35; 33C45In recent years, much attention has been paid to the role of classical special functions of a real or complex variable in mathematical physics, especially in boundary value problems (BVPs). In the present paper, we propose a higher-dimensional analogue of the generalized Bessel polynomials within Clifford analysis via a special set of monogenic polynomials. We give the definition and derive a number of important properties of the generalized monogenic Bessel polynomials (GMBPs), which are defined by a generating exponential function and are shown to satisfy an analogue of Rodrigues' formula. As a consequence, we establish an expansion of particular monogenic functions in terms of GMBPs and show that the underlying basic series is everywhere effective.We further prove a second-order homogeneous differential equation for these polynomials.

The generalization of Rodrigues’ formula for orthogonal matrix polynomials has attracted the attention of many researchers. This generalization provides new integral and differential representations in addition to new mathematical results that are useful in theoretical and numerical computations. Using a recently studied operational matrix for shifted Legendre polynomials with the variable coefficients fractional differential equations, the present work introduces the shifted Legendre-type matrix polynomials of arbitrary (fractional) orders utilizing some Rodrigues matrix formulas. Many interesting mathematical properties of these matrix polynomials are investigated and reported in this paper, including recurrence relations, differential properties, hypergeometric function representation, and integral representation. Furthermore, the orthogonality property of these polynomials is examined in some particular cases. The developed results provide a matrix framework that generalizes and enhances the corresponding scalar version and introduces some new properties with proposed applications. Some of these applications are explored in the present work.

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In this paper, we contribute to the results of Bakhet et al. (Integral Transforms Spec. Funct. 30:138–156, 2019) by applying fractional operators to the Wright hypergeometric matrix functions. We give matrix recurrence relations and integral formulas for the Wright hypergeometric matrix functions. We also clarify particular cases of the main results.