We present conditions under which all solutions of the fractional differential equation with the Caputo derivative D ax(t) = f(t, x(t)), a > 1, α ∈ (1, 2), (1) are asymptotic to at+ b as t → ∞ for some real numbers a, b. AMS Classification: 34E10, 34A34

The space-time-fractional diffusion equation with the Caputo time-fractional derivative and Riesz fractional Laplacian is considered in the case of axial symmetry. Mass absorption (mass release) is described by a source term proportional to concentration. The integral transform technique is used. Different particular cases of the solution are studied. The numerical results are illustrated graph...

In this article, we consider a fractional differential equation (FDE) with Caputo derivative and study the existence and continuation of its solution. Firstly, we prove a theorem on the existence of local solutions. Then we extend the continuation theorems for ODEs to those FDEs. Also several global existence results for FDE are obtained.

The current study is of interest when performing a useful extension crucial physical problem through non-local singular fractional operator. We provide solutions that include three arbitrary parameters α, ρ, and γ for the Resistance-Capacitance (RC), Inductance-Capacitance (LC), Resistance-Inductance-Capacitance (RLC) electric circuits utilizing generalized type operator in sense Caputo, called...

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.