The aim of this paper is to study the fractional Hadamard inequalities for Caputo fractional derivatives of strongly convex functions. We obtain refinements of two known fractional versions of the Hadamard inequality for convex functions. By applying identities for Caputo fractional derivatives we get refinements of error bounds of these inequalities. The given results simultaneously provide refinements as well as generalizations of already known inequalities.

The recently introduced class of vertex-degree-based molecular structure descriptors, called Sombor indices (\(SO\)), are examined and a few of their basic properties established. Simple lower and upper bounds for \(SO\) are determined. It is shown that any vertex–degree–based descriptor can be viewed as a special case of a Sombor-type index.

This paper considers the extension of the Adomian decomposition method (ADM) for solving nonlinear ordinary differential equations of constant coefficients to those equations with variable coefficients. The total derivatives of the nonlinear functions involved in the problem considered were derived in order to obtain the Adomian polynomials for the problems. Numerical experiments show that Adomian decomposition method can be extended as alternative way for finding numerical solutions to ordinary differential equations of variable coefficients. Furthermore, the method is easy with no assumption and it produces accurate results when compared with other methods in literature.

In this paper, we introduce a new class of analytic functions by using the lambda operator and obtain some subordination results.

In this paper, we introduce the notion of modified Suzuki-Edelstein-Geraghty proximal contraction and prove the existence and uniqueness of best proximity point for such mappings. Our results extend and unify many existing results in the literature. We draw corollaries and give illustrative example to demonstrate the validity of our result.

In this paper, we give characterizations of certain properties of inner product type integral transformers. We first consider unitarily invariant norms and operator valued functions. We then give results on norm inequalities for inner product type integral transformers in terms of Landau inequality, Grüss inequality. Lastly, we explore some of the applications in quantum theory.

Novel coronavirus likewise called COVID-19 began in Wuhan, China in December 2019 and has now outspread over the world. Around 63 millions of people currently got influenced by novel coronavirus and it causes around 1,500,000 deaths. There are just about 600,000 individuals contaminated by COVID-19 in Bangladesh too. As it is an exceptionally new pandemic infection, its diagnosis is challenging for the medical community. In regular cases, it is hard for lower incoming countries to test cases easily. RT-PCR test is the most generally utilized analysis framework for COVID-19 patient detection. However, by utilizing X-ray image based programmed recognition can diminish the expense and testing time. So according to handling this test, it is important to program and effective recognition to forestall transmission to others. In this paper, author attempts to distinguish COVID-19 patients by chest X-ray images. Author executes various pre-trained deep learning models on the dataset such as Base-CNN, ResNet-50, DenseNet-121 and EfficientNet-B4. All the outcomes are compared to determine a suitable model for COVID-19 detection using chest X-ray images. Author also evaluates the results by AUC, where EfficientNet-B4 has 0.997 AUC, ResNet-50 has 0.967 AUC, DenseNet-121 has 0.874 AUC and the Base-CNN model has 0.762 AUC individually. The EfficientNet-B4 has achieved 98.86% accuracy.

Let \(G=(V,E)\) be a graph. Then the first and second entire Zagreb indices of \(G\) are defined, respectively, as \(M_{1}^{\varepsilon}(G)=\displaystyle \sum_{x \in V(G) \cup E(G)} (d_{G}(x))^{2}\) and \(M_{2}^{\varepsilon}(G)=\displaystyle \sum_{\{x,y\}\in B(G)} d_{G}(x)d_{G}(y)\), where \(B(G)\) denotes the set of all 2-element subsets \(\{x,y\}\) such that \(\{x,y\} \subseteq V(G) \cup E(G)\) and members of \(\{x,y\}\) are adjacent or incident to each other. In this paper, we obtain the entire Zagreb indices of the line graph and line cut-vertex graph of the subdivision graph of the friendship graph.

Our purpose in this paper is to use \(\psi-\)Riemann-Liouville fractional integral operator which is the fractional integral of any function with respect to another increasing function to establish some new fractional integral inequalities of Hermite-Hadamard, involving concave functions. Using the concave functions, we establish some new fractional integral
inequalities related to the Hermite-Hadamard type inequalities via \(\psi-\)Riemann-Liouville fractional integral operator.

Consider a class of two-point Boundary Value Problems (BVP) for a stochastic nonlinear fractional order differential equation \(D^\alpha u(t)=\lambda\sqrt{I^\beta[\sigma^2(t,u(t))]}\dot{w}(t),\,\,0<t<1\) with boundary conditions \(u(0)=0,\,\,u'(0)=u'(1)=0,\) where \(\lambda>0\) is a level of the noise term, \(\sigma:[0,1]\times\mathbb{R}\rightarrow\mathbb{R}\) is continuous, \(\dot{w}(t)\) is a generalized derivative of Wiener process (Gaussian white noise), \(D^\alpha\) is the Riemann-Liouville fractional differential operator of order \(\alpha\in (3,4)\) and \(I^\beta,\,\,\beta>0\) is a fractional integral operator. We formulate the solution of the equation via a stochastic Volterra-type equation and investigate its existence and uniqueness under some precise linearity conditions using contraction fixed point theorem. A case of the above BVP for a stochastic nonlinear second order differential equation for \(\alpha=2\) and \(\beta=0\) with \(u(0)=u(1)=0\) is also studied.