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Dive into the research topics where Mirjana Stojanović is active.

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Featured researches published by Mirjana Stojanović.


Journal of Vibration and Control | 2007

The Two Forms of Fractional Relaxation of Distributed Order

Francesco Mainardi; Antonio Mura; Rudolf Gorenflo; Mirjana Stojanović

The first-order differential equation of exponential relaxation can be generalized by using either the fractional derivative in the Riemann—Liouville (R-L) sense and in the Caputo (C) sense, both of a single order less than 1. The two forms turn out to be equivalent. When, however, we use fractional derivatives of distributed order (between zero and 1), the equivalence is lost, in particular on the asymptotic behaviour of the fundamental solution at small and large times. We give an outline of the theory providing the general form of the solution in terms of an integral of Laplace type over a positive measure depending on the order-distribution. We consider in some detail two cases of fractional relaxation of distribution order: the double-order and the uniformly distributed order discussing the differences between the R-L and C approaches. For all the cases considered we give plots of the solutions for moderate and large times.


Fractional Calculus and Applied Analysis | 2013

Fundamental solution of a distributed order time-fractional diffusion-wave equation as probability density

Rudolf Gorenflo; Yuri Luchko; Mirjana Stojanović

AbstractIn this paper, the Cauchy problem for the spatially one-dimensional distributed order diffusion-wave equation


Journal of Computational and Applied Mathematics | 1988

Solving singularly perturbed boundary-value problems by spline in tension

Katarina Surla; Mirjana Stojanović

\int_0^2 {p(\beta )D_t^\beta u(x,t)d\beta } = \frac{{\partial ^2 }} {{\partial x^2 }}u(x,t)


Journal of Computational and Applied Mathematics | 2011

Numerical method for solving diffusion-wave phenomena

Mirjana Stojanović

is considered. Here, the time-fractional derivative Dtβ is understood in the Caputo sense and p(β) is a non-negative weight function with support somewhere in the interval [0, 2]. By employing the technique of the Fourier and Laplace transforms, a representation of the fundamental solution of the Cauchy problem in the transform domain is obtained. The main focus is on the interpretation of the fundamental solution as a probability density function of the space variable x evolving in time t. In particular, the fundamental solution of the time-fractional distributed order wave equation (p(β) ≡ 0, 0 ≤ β < 1) is shown to be non-negative and normalized. In the proof, properties of the completely monotone functions, the Bernstein functions, and the Stieltjes functions are used.


Integral Transforms and Special Functions | 2011

Convolution-type derivatives and transforms of Colombeau generalized stochastic processes

Danijela Rajter-Ćirić; Mirjana Stojanović

The difference scheme via spline in tension for the problem: − ϵy″ + p(x)y = f(x), p(x)\s>0, y(0) = α0, y(1) = α1, is derived. The error of the form O(h min(h, √ϵ) is obtained. When p(x) = p = const., the corresponding spline in tension achieves the second order of the global uniform convergence.


Applied Numerical Mathematics | 1996

Splines difference methods for a singular perturbation problem

Mirjana Stojanović

We find solutions for the diffusion-wave problem in 1D with n-term time fractional derivatives whose orders belong to the intervals (0,1),(1,2) and (0,2) respectively, using the method of the approximation of the convolution by Laguerre polynomials in the space of tempered distributions. This method transfers the diffusion-wave problem into the corresponding infinite system of linear algebraic equations through the coefficients, which are uniquely solvable under some relations between the coefficients with index zero. The method is applicable for nonlinear problems too.


Bit Numerical Mathematics | 1990

Numerical solution of a singularly perturbed problem via exponential splines

Mirjana Stojanović

In this paper, we introduce a theory of convolution-type (fractional) derivatives in the algebra of Colombeau generalized stochastic processes. Non-regularized and regularized Caputo fractional derivatives of Colombeau generalized stochastic processes are introduced and some of their properties are studied. As an example, a certain stochastic Cauchy problem is considered in two cases, with nonregularized and regularized Caputo fractional derivatives.


Integral Transforms and Special Functions | 2006

Fractional differential equations through Laguerre expansions in abstract spaces: error estimates

Stevan Pilipović; Mirjana Stojanović

Abstract We present a class of splines difference schemes for non-self-adjoint singular perturbation problem. They are uniform, optimal or ϵ-convergent in a small parameter ϵ. We give an error bound. We present the numerical examples to confirm it.


Central European Journal of Physics | 2013

Singular fractional evolution differential equations

Mirjana Stojanović

It is proved that a spline difference scheme for a singularly perturbed self-adjoint problem, derived by using exponential cubic splines at mid-points, has second order uniform convergence in a small parameter ε. Numerical experiments are presented to confirm the theoretical predictions.


Fractional Calculus and Applied Analysis | 2011

Fractional derivatives in spaces of generalized functions

Mirjana Stojanović

An approximation procedure by the means of expansion with respect to Laguerre orthogonal basis of the space is given. It is applied to solutions of a class of convolution equations, by transforming them to corresponding systems of algebraic equations for the coefficients. Especially, Volterra-type integral and integro-differential equations and system of equations with fractional derivatives modeling viscoelastic rod are solved. Error estimates depending on the order of approximation are derived.

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Rudolf Gorenflo

Free University of Berlin

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Yuri Luchko

Beuth University of Applied Sciences Berlin

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