Application of fractional differential equations in mathematical modelling

A fractional model for malaria transmission under control program is analysed. The integer order model introduced by Chityaka et al. (2008) is discussed and later modified for a fractional order model. For the improvement and continuance of chronic liver cirrhosis, viral hepatitis (hepatitis B and C) is the major risk factor. For prohibiting the numerical scheme of the fractional order model, the Adams- type predictor- evaluate-connector-evaluate approach is applied. Severe acute respiratory syndrome coronavirus 2(SARS-COV-2) which is a new strain of deadly disease coronavirus is the main factor for COVID-19. Three populations - the uninfected epithelial cells, infected cells and the SARS-COV-2 virus are analysed. Differential equation on mathematical modelling is taken as a quality perspective for analysing and predicting treatment outcomes for population-level and patient -specific responses. To analyse the advantages and limitations of presenting fractional derivatives into three standard models of tumour growth, patient data of radiation- treated tumours is applied. When the sugar level in blood is improper metabolic disorder Diabetes Mellitus will appear and is classified into 3 main types. A model of Diabetes Mellitus Type SEIIT is provided by discussing treatment and generic factors. A new fractional mathematical model is created via recent improved fractional and integral operators. Other operators such as Caputo Riemann- Liouville, Katuganpola, Jarad and Hadamard are extended and generalized by applying these improved- fractional differential and integral operators along with the various kinds of Ulam stability for the considered fractional HIV model of fractional mathematical modelling. To analyse the influence of treatment adherence as well as awareness on the spread of tuberculosis (TB), a new deterministic disease system is created. The proposed new model is categorised into 6 different groups and they are analysed in the Caputo fractional operator sense. For the improvement and progression of chronic liver cirrhosis, viral hepatitis (hepatitis B and C) is the major risk factor. The symptomatic stage is by complex disorder affecting multiple systems of liver organ with hospitalization is the characteristic of the symptom stage of cirrhosis. For preventing the numerical scheme of the fractional order model, the Adams- type predictor- evaluate-connector-evaluate approach is applied.