# American Institute of Mathematical Sciences

## Mathematical model of diabetes and its complication involving fractional operator without singular kernal

 1 Departement of Mathematics, Amity School Of Applied Sciences, Amity University Rajasthan, Jaipur-303002, India 2 School of Liberal Studies, Ambedkar University Delhi, Delhi-110006, India

* Corresponding author: Pranay Goswami

Received  April 2019 Revised  July 2019 Published  November 2019

Diabetes is one of the burning issues of the whole world. It effected the world population rapidly. According to the WHO approx 415 million people are living with diabetes in the world and this figure is expected to rise up to 642 million by 2040. World various organizations raise their voice against the dire facts about the increasing graph of diabetes and its complicated patients. In this paper authors define the fractional model of diabetes and its complications involving to fractional operator with exponential kernel. The authors discuss the existence of the solution by using fixed point theorem and also show the uniqueness of the solution. To validate the model's efficiency the authors provided numerical simulation by using HPM. To strengthen the model the results have been presented in the form of graphs.

Citation: Ravi Shanker Dubey, Pranay Goswami. Mathematical model of diabetes and its complication involving fractional operator without singular kernal. Discrete & Continuous Dynamical Systems - S, doi: 10.3934/dcdss.2020144
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Flow Chart
Represents for the behavior of the solution C(t), with respect to t for different values of other perimeter defined above
Represents for the behavior of the solution E(t), with respect to t for different values of other perimeter defined above
Table-1
 A(t) The incidence of Diabetes Mellitus B(t) Number of person having diabetics without complications C(t) Number of person having diabetics with complications E(t) Size of population of diabetics at time $t$ $\delta$ The probability of a person having diabetic and developing complications $\varepsilon$ Natural rate of mortality $\lambda$ Rate of complications are recovered $\upsilon$ Rate of diabetic patients having complication and become severely disabled $\mu$ Rate of mortality due to diabetic complications
 A(t) The incidence of Diabetes Mellitus B(t) Number of person having diabetics without complications C(t) Number of person having diabetics with complications E(t) Size of population of diabetics at time $t$ $\delta$ The probability of a person having diabetic and developing complications $\varepsilon$ Natural rate of mortality $\lambda$ Rate of complications are recovered $\upsilon$ Rate of diabetic patients having complication and become severely disabled $\mu$ Rate of mortality due to diabetic complications