A fractional order HIV model with both virus-tocell and cell-to-cell transmissions and therapy effect is investigated. The conditions for the existence of the equilibria are determined. Local stability analysis of the HIV model is studied by using the fractional Routh-Hurwitz stability conditions. We have generalized the integer LaSalle’s invariant theorem into fractional system and given some ...

The L-cosine transform of an even, continuous function f ∈ Ce(S ) is defined by: H(x) = ∫ S |〈x, ξ〉|f(ξ) dξ, x ∈ R. It is shown that if p is not an even integer then all partial derivatives of even order of H(x) up to order p + 1 (including p + 1 if p is an odd integer) exist and are continuous everywhere in R\{0}. As a result of the corresponding differentiation formula, we show that if f is a...

Remark: By the same reasoning, if one replaces 2016 in the problem by a general integer N, then the minimum value of j is the smallest one for which N divides j!. This can be deduced from Pólya’s observation that the set of integer-valued polynomials is the free Zmodule generated by the binomial polynomials (x n ) for n = 0,1, . . . . That statement can be extended to polynomials evaluated on a...

The paper must have abstract. In this paper, we present an approximate analytical algorithm to solve non-linear quadratic Riccati differential equations of fractional order based on the optimal homotopy asymptotic method (OHAM). OHAM has the benefit of adjusting the convergence rate and the region of the solution series via several auxiliary parameters over the homotopy analysis method (HAM) th...

to hold for functions u satisfying given (possibly void) boundary conditions, where the Ak are linear partial differential operators, p is greater than one, and || • j | , , 3 , is an L p norm defined for all real values of 5. When 5 is a non-negative integer, ||w||8fl, is essentially the sum of the L norms of u and all its derivatives up to order s. We do not require that the A * be of the sam...

Two exponential wave integrator Fourier pseudospectral (EWI-FP) methods are presented and analyzed for the long-time dynamics of Dirac equation with small potentials characterized by ??(0,1] a dimensionless parameter. Based on (symmetric) temporal derivatives in phase space followed applying discretization spatial derivatives, EWI-FP explicit spectral accuracy second-order time any fixed ?=?0. ...

Abstract This article considers a fractional-order neuron model under an electromagnetic field in terms of generalized Caputo fractional derivatives. The motivation for incorporating derivatives the previously proposed integer-order is that impresses with efficient effects memory, and parameters orders can increase performance by amplifying degree freedom. results on uniqueness solution are est...

Abstract In this paper we introduce a fractional variant of the characteristic function random variable. It exists on whole real line, and is uniformly continuous. We show that moments can be expressed in terms Riemann–Liouville integrals derivatives function. The are interest particular for distributions whose integer do not exist. Some illustrative examples also presented.

For integral representations of associated Legendre functions in terms of modified Bessel functions, we establish justification for differentiation under the integral sign with respect to parameters. With this justification, derivatives for associated Legendre functions of the first and second kind with respect to the degree are evaluated at odd-halfinteger degrees, for general complex-orders, ...

Fractional derivatives provide an excellent tool for the description of memory and hereditary properties of various materials and processes. These characteristics of the fractional derivatives make the fractional-order models more realistic and practical than the classical integer-order models. In recent years, boundary value problems for nonlinear fractional differential equations have been ad...