Some Caputo q-fractional difference equations are solved. The solutions are expressed by means of a new introduced generalized type of q-Mittag-Leffler functions. The method of successive approximation is used to obtain ...

In this paper, we present a new fractional-order mathematical model for a tumor-immune surveillance mechanism. We analyze the interactions between various tumor cell populations and immune system via a system of fractional ...

The aim of this paper is to develop a fractional order mathematical model for describing the spread of hepatitis B virus (HBV). We also provide a rigorous mathematical analysis of the stability of the disease-free equilibrium ...

We apply generalized operators of fractional integration involving Appell's function F-3(.) due to Marichev-Saigo-Maeda, to the product of the generalized Bessel function of the first kind due to Baricz. The results are ...

The classical Nambu mechanics is generalized to involve fractional derivatives using two different methods. The first method is based on the definition of fractional exterior derivative and the second one is based on ...

The fractional calculus has gained considerable importance in various fields of science and engineering, especially during the last few decades. An open issue in this emerging field is represented by the fractional variational ...

The Hamiltonian formulation of Lagrangian on time scale is investigated and the equivalence of Hamilton and Euler-Lagrange equations is obtained. The role of Lagrange multipliers is discussed

We apply the lower and upper solutions method and fixed-point theorems to prove the existence of positive solution to fractional boundary value problem D(0+)(alpha)u(t) + f(t, u(t)) = 0, 0 < t < 1, 2 < alpha <= 3, u(0) = ...

This paper presents a new mathematical formulation in fractional sense describing the asymptotic behavior of immunogenic tumor growth. The new model is investigated through different fractional operators with and without ...

A class of interval-valued fractional nonlinear differential equations is proposed in this paper. The system is reduced to two kinds of standard fractional differential equations if w -monotone conditions are provided. ...