558 research outputs found
Fractional calculus modelling for unsteady unidirectional flow of incompressible fluids with time-dependent viscosity
In this note we analyze a model for a unidirectional unsteady flow of a
viscous incompressible fluid with time dependent viscosity. A possible way to
take into account such behaviour is to introduce a memory formalism, including
thus the time dependent viscosity by using an integro-differential term and
therefore generalizing the classical equation of a Newtonian viscous fluid. A
possible useful choice, in this framework, is to use a rheology based on
stress/strain relation generalized by fractional calculus modelling. This is a
model that can be used in applied problems, taking into account a power law
time variability of the viscosity coefficient. We find analytic solutions of
initial value problems in an unbounded and bounded domain. Furthermore, we
discuss the explicit solution in a meaningful particular case
Necessary and sufficient conditions for the fractional calculus of variations with Caputo derivatives
We prove optimality conditions for different variational functionals
containing left and right Caputo fractional derivatives. A sufficient condition
of minimization under an appropriate convexity assumption is given. An
Euler-Lagrange equation for functionals where the lower and upper bounds of the
integral are distinct of the bounds of the Caputo derivative is also proved.
Then, the fractional isoperimetric problem is formulated with an integral
constraint also containing Caputo derivatives. Normal and abnormal extremals
are considered.Comment: Submitted 6/March/2010 to Communications in Nonlinear Science and
Numerical Simulation; revised 12/July/2010; accepted for publication
16/July/201
Approximate Analytical Solutions of Space-Fractional Telegraph Equations by Sumudu Adomian Decomposition Method
The main goal in this work is to establish a new and efficient analytical scheme for space fractional telegraph equation (FTE) by means of fractional Sumudu decomposition method (SDM). The fractional SDM gives us an approximate convergent series solution. The stability of the analytical scheme is also studied. The approximate solutions obtained by SDM show that the approach is easy to implement and computationally very much attractive. Further, some numerical examples are presented to illustrate the accuracy and stability for linear and nonlinear cases
Fractional Calculus - Theory and Applications
In recent years, fractional calculus has led to tremendous progress in various areas of science and mathematics. New definitions of fractional derivatives and integrals have been uncovered, extending their classical definitions in various ways. Moreover, rigorous analysis of the functional properties of these new definitions has been an active area of research in mathematical analysis. Systems considering differential equations with fractional-order operators have been investigated thoroughly from analytical and numerical points of view, and potential applications have been proposed for use in sciences and in technology. The purpose of this Special Issue is to serve as a specialized forum for the dissemination of recent progress in the theory of fractional calculus and its potential applications
Series Solutions of Multi-Term Fractional Differential Equations
In this thesis, we introduce a new series solutions for multi-term fractional differential equations of Caputo’s type. The idea is similar to the well-known Taylor Series method, but we overcome the difficulty of computing iterated fractional derivatives, which do not commuted in general. To illustrate the efficiency of the new algorithm, we apply it for several types of multi-term fractional differential equations and compare the results with the ones obtained by the well-known Adomian decomposition method (ADM)
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