Integrals and derivatives of fractional order have found many applications in recent studies in science. The interest in fractals and fractional analysis has been growing continually in the last few years. Fractional derivatives and integrals have numerous applications: kinetic theories [1, 2, 3]; statistical mechanics [4, 5, 6]; dynamics in complex media [7, 8, 9, 10, 11]; electrodynamics [12,...

In this article, we survey the asymptotic stability analysis of fractional differential systems with the Prabhakar fractional derivatives. We present the stability regions for these types of fractional differential systems. A brief comparison with the stability aspects of fractional differential systems in the sense of Riemann-Liouville fractional derivatives is also given. 

The metabolism of the fifth component of complement (C5), and its relatonship to metabolism of the third component of complement (C3), has been studied in normal subjects and patients by simultaneous administration of radioiodine labeled C5 and C3. In seven normal subjects the fractional catabolic rate of C5 ranged from 1.5 to 2.1% of the plasma pool/h and extravascular/intravascular distributi...

Stebbings, J. H. (1974). Thorax, 29, 505-510. Fractional carbon monoxide uptake in an employed population. The fractional carbon monoxide uptake in 913 New York City transit workers was studied. A prediction equation for white males, based on nonsmokers, was obtained: fractional CO uptake= 0 58032-0000204 x age+ 0 0004 x weight (kilograms). Weight was the index of body size most strongly correl...

in this paper, under appropriate oscillating behaviours of the nonlinear term, we prove some multiplicity results for a class of nonlinear fractional equations. these problems have a variational structure and we find three solutions for them by exploiting an abstract result for smooth functionals defined on a reflexive banach space. to make the nonlinear methods work, some careful analysis of t...

in this paper we apply hybrid functions of general block-pulse‎ ‎functions and legendre polynomials for solving linear and‎ ‎nonlinear multi-order fractional differential equations (fdes)‎. ‎our approach is based on incorporating operational matrices of‎ ‎fdes with hybrid functions that reduces the fdes problems to‎ ‎the solution of algebraic systems‎. ‎error estimate that verifies a‎ ‎converge...

in this paper, a new numerical method for solving fractional optimal control problems (focps) is presented. the fractional derivative in the dynamic system is described in the caputo sense. the method is based upon biorthogonal cubic hermite spline multiwavelets approxima-tions. the properties of biorthogonal multiwavelets are first given. the operational matrix of fractional riemann-lioville i...