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...

As technology advances and the Internet makes our world a global village, it is important to understand prospective career of freelancing. A novel symmetric fractional mathematical model introduced in this study describe competitive market freelancing significance information its acceptance. In study, fixed point theory applied analyze uniqueness existence freelance model. Its numerical solutio...

In this paper we propose a necessary condition for the existence of chaos in delay differential equations of fractional order. To explain the proposed theory, we discuss fractional order Liu system and financial system involving delay. Keywords—Caputo derivative, delay, stability, chaos.

This paper deals with the stability of nonlinear fractional differential systems equipped with the Caputo derivative. At first, a sufficient condition on asymptotical stability is established by using a Lyapunov-like function. Then, the fractional differential inequalities and comparison method are applied to the analysis of the stability of fractional differential systems. In addition, some ot...

In this paper, we investigate the numerical solution of fractional integro-differential equations by comparison between He’s variational iteration method and taylor expansion method. The fractional derivative is described in the Caputo sense. Some numerical examples are presented to illustrate the methods.

In this paper, a modification of variational iteration method is applied to solve fractional integro-differential equations. The fractional derivative is considered in the Caputo sense. Through examples, we will see the modified method performs extremely effective in terms of efficiency and simplicity to solve fractional integro-differential equations. 2000 Mathematics Subject Classification: 6...

This paper presents the necessary optimality conditions of Euler–Lagrange type for variational problems with natural boundary conditions and problems with holonomic constraints where the fuzzy fractional derivative is described in the combined Caputo sense. The new results are illustrated by computing the extremals of two fuzzy variational problems. AMS subject classifications: 65D10, 92C45

In this paper we use the upper and lower solutions method to investigate the existence of solutions of a class of impulsive partial hyperbolic differential inclusions at fixed moments of impulse involving the Caputo fractional derivative. These results are obtained upon suitable fixed point theorems.

This paper is devoted to study the existence of solutions for a class of initial value problems for impulsive fractional differential equations involving the Caputo fractional derivative in a Banach space. The arguments are based upon Mönch’s fixed point theorem and the technique of measures of noncompactness.

We consider infinite horizon fractional variational problems, where the fractional derivative is defined in the sense of Caputo. Necessary optimality conditions for higher-order variational problems and optimal control problems are obtained. Transversality conditions are obtained in the case state functions are free at the initial time.