Tumor diseases have killed many people around the world for centuries. For this purpose, a lot of scientists analyzed immune system’s cells in order to cope with tumor growths living beings. reason, we examine system reflecting relationship between and growth study. This is handled traditional Caputo fractional derivative. We give stability analysis equilibrium points solution properties system...

There are many functions which are continuous everywhere but non-differentiable at someor all points such functions are termed as unreachable functions. Graphs representing suchunreachable functions are called unreachable graphs. For example ECG is such an unreachable graph. Classical calculus fails in their characterization as derivatives do not exist at the unreachable points. Such unreachabl...

Supported by the National Eye Institute, National Institutes of Health, Bethesda, Maryland (cooperative agreement nos.: U10 EY017823, U10 EY017825, U10 EY017826, and U10 EY017828). The funding organization participated in the design and conduct of the study, data analysis and interpretation, and review of the manuscript. Author Contributions: Conception and design: Maguire, Martin, Ying, Jaffe,...

The purpose of this paper is to make a contribution for solving one of the major drawbacks for using fractional controllers: the controller implementation. In digital form, this is usually done by using a truncated version of the Grundwald-Letnikov formula for fractional derivative. In this work, experimental results are given comparing this method for digital implementation of a fractional PD ...

This paper presents a new numerical method to solve time fractional Fokker-Planck equation. The space dimension is discretized to the Gauss-Lobatto points, then we apply pseudo-spectral successive integration matrix for this dimension. This approach shows that with less number of points, we can approximate the solution with more accuracy. The numerical results of the examples are displayed.

In this paper, we study optimal control problems for nonlinear fractional order boundary value on a star graph, where the derivative is described in Caputo sense. The adjoint state and optimality system are derived problem (FOCP) by using Lagrange multiplier method. Then, existence uniqueness of solution equation proved means Banach contraction principle. We also pr...

In this paper, we presented a novel multi-strain TB model of variable-order fractional derivatives, which incorporates three strains: drug-sensitive, emerging multi-drug resistant (MDR) and extensively drug-resistant (XDR), as an extension for multi-strain TB model of nonlinear ordinary differential equations which developed in 2014 by Arino and Soliman [1]. Numerical simulations for this varia...

An optimal control problem for the variable-order fractional-integer mathematical model of vaccination Covid 19 is presented in this research, where order derivatives varies during course time interval, becoming fractional or classical when it more favourable. The are defined here using both integral Riemann–Liouville and Caputo derivative. existence, uniqueness, boundedness positivity solution...

Decoupled fractional Laplacian wave equation can describe the seismic wave propagation in attenuating media. Fourier pseudospectral implementations, which solve the equation in spatial frequency domain, are the only existing methods for solving the equation. For the earth media with curved boundaries, the pseudospectral methods could be less attractive to handle the irregular computational doma...

Article history: Received 1 June 2014 Received in revised form 15 April 2015 Accepted 29 April 2015 Available online 5 May 2015