Solvability and Ulam-Hyers stability analysis for nonlinear piecewise fractional cancer dynamic systems

Abstract

We examine a nonlinear dynamical model that depicts the interaction between cancerous cells and an oncolytic virus. For best modelling the disease, we use the Caputo fractional derivative in piecewise approaches. By employing piecemeal techniques, we treat a compartment in the body that contains infectious and non-infectious cells. More precisely, the solvability and Ulam-Hyers (U-H) stability results are considered using standard concepts. Further, to support our investigation with numerical results, we apply the Euler method to develop an approximation solution. It connected with numerous graphical representations of the system using various arbitrary ordering and varying values of the isolation parameters. Here we remark that the multi-step behavior that certain problems exhibit, is one of important issues naturally. This paper introduces the idea of piecewise derivative with the goal of modeling real-world issues that follow multiples processes. With the help of the used approach, we investigate the cancer disease model and its transmission dynamical behavior with crossover effect.

Fractional-Order Dynamics in Epidemic Disease Modeling with Advanced Perspectives of Fractional Calculus

“…Applying identical reasoning as in (26) to approximate the rest equations of model ( 4), we arrive at…”

“…To explore the concept of fractional calculus in epidemic modeling, we refer to [18][19][20][21]. For the recent advances in fractional-order mathematical models with a piecewise fractional differential operator, we refer to [22][23][24][25][26].…”