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A brain tumor can have an impact on the symmetry of a person's face or head, depending on its location and size. If a brain tumor is located in an area that affects the muscles responsible for facial symmetry, it can cause asymmetry. However, not all brain tumors cause asymmetry. Some tumors may be located in areas that do not affect facial symmetry or head shape. Additionally, the asymmetry caused by a brain tumor may be subtle and not easily noticeable, especially in the early stages of the condition. Brain tumor classification using deep learning involves using artificial neural networks to analyze medical images of the brain and classify them as either benign (not cancerous) or malignant (cancerous). In the field of medical imaging, Convolutional Neural Networks (CNN) have been used for tasks such as the classification of brain tumors. These models can then be used to assist in the diagnosis of brain tumors in new cases. Brain tissues can be analyzed using magnetic resonance imaging (MRI). By misdiagnosing forms of brain tumors, patients' chances of survival will be significantly lowered. Checking the patient's MRI scans is a common way to detect existing brain tumors. This approach takes a long time and is prone to human mistakes when dealing with large amounts of data and various kinds of brain tumors. In our proposed research, Convolutional Neural Network (CNN) models were trained to detect the three most prevalent forms of brain tumors, i.e., Glioma, Meningioma, and Pituitary; they were optimized using Aquila Optimizer (AQO), which was used for the initial population generation and modification for the selected dataset, dividing it into 80% for the training set and 20% for the testing set. We used the VGG-16, VGG-19, and Inception-V3 architectures with AQO optimizer for the training and validation of the brain tumor dataset and to obtain the best accuracy of 98.95% for the VGG-19 model. [ABSTRACT FROM AUTHOR]

The object of investigation in this paper is a scalar linear fractional differential equation with generalized proportional derivative of Riemann–Liouville type (LFDEGD). The main goal is the obtaining an explicit solution of the initial value problem of the studied equation. Note that the locally solvability, being the same as the existence of solutions to the initial value problem, is connected with the symmetry of a transformation of a system of differential equations. At the same time, several criteria for existence of the initial value problem for nonlinear fractional differential equations with generalized proportional derivative are connected with the linear ones. It leads to the necessity of obtaining an explicit solution of LFDEGD. In this paper two cases are studied: the case of no impulses in the differential equation are presented and the case when instantaneous impulses at initially given points are involved. All obtained formulas are based on the application of Mittag–Leffler function with two parameters. In the case of impulses, initially the appropriate impulsive conditions are set up and later the explicit solutions are obtained. [ABSTRACT FROM AUTHOR]

This paper deals with a new class of hybrid fractional differential equations with fractional proportional derivatives of a function with respect to a certain continuously differentiable and increasing function ϑ. By means of a hybrid fixed point theorem for a product of two operators, an existence result is proved. Furthermore, the sufficient conditions of the continuous dependence on the given parameters are investigated. Finally, a simulative example is given to highlight the acquired outcomes. [ABSTRACT FROM AUTHOR]