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In this study, we derive an optimal control problem for schistosomiasis disease by using Caputo fractional derivative. In the formulation of the proposed control problem, we use the concept of Pontryagin’s minimum principle and the Hamiltonian. To minimize the infected bovine population, we use vaccination, the release of competitor snails, chlorination of water, and treatment controls. The forward-backward sweep method is used to derive the numerical solution of the proposed problem. The parameter values based on real data are used to plot a number of figures. The objective of this paper is to explore the possibilities of controlling the spread of schistosomiasis disease. The presence of the Caputo fractional operator includes the memory in the model which is the main motivation behind the proposed fractional-order generalization.

Nowadays, the mathematical modeling of infectious diseases is a big trend worldwide. The mathematical models help us to forecast future outbreaks of diseases in the presence of present data. In this article, we represent a model of the transmission of Chlamydia in the United States by using data from 1989 to 2019. In the formulation of the model, we used integer and fractional derivatives. Several graphs are plotted for the various possible cases of the given parameters. The aim of this paper is to justify how the mathematical models in terms of fractional derivatives have more degree of freedom to explore disease dynamics for a particular data set and capture memory effects. The separate parameter estimation for each value of the fractional order increases the novelty of this work. The use of a real-data set of Chlamydia in the United States makes this study more visible and important to the literature.

The idea behind this study is to investigate the controllability of dynamical systems in terms of the ψ-Caputo fractional derivative. The Grammian matrix is used to get at necessary and sufficient controllability requirements for linear systems, which are characterized by the Mittag-Leffler functions, while the fixed point approach is used to arrive at adequate controllability criteria for nonlinear systems. The novelty of this research is to inquire into the controllability concepts by utilizing the ψ-Caputo fractional derivative. Since ψ-Caputo fractional derivatives have the advantage of capturing memory effects as well as increasing the accuracy of anticipating real-world scenarios. A few numerical examples are offered to help better understand the theoretical results.

In this article, we define a mathematical model to analyze the outbreaks of the most deadly disease of the decade named 2019‐nCoV by using integer and fractional order derivatives. For the case study, the real data of Russia is taken to perform novel parameter estimation by using the Trust Region Reflective (TRR) algorithm. First, we define an integer order model and then generalize it by using fractional derivatives. A novel optimal control problem is derived to see the impact of possible preventive measures against the spread of 2019‐nCoV. We implement the forward–backward sweep method to numerically solve our proposed model and control problem. A number of graphs have been plotted to see the impact of the proposed control practically. The Russian data‐based parameter estimation along with the proposal of a mathematical model in the sense of Caputo fractional derivative that contains the memory term in the system are the main novel features of this study.