Numerical Methods for Solving Fractional Differential Problems

Dear Colleagues,

In recent decades, fractional calculus increased its popularity due to the awareness that many physical problems, such as viscoelasticity, Brownian motions, and so on, need fractional derivatives to be modeled. For some problems, there are analytical solutions. These are expressed through the Mittag Leffer function, which is a series expansion and thus needs to be computed with numerical tools. For this reason and for the other unsolved problems, the literature has identified many ways to numerically solve fractional differential problems. Many methods use finite difference for the integer derivative and the quadrature rule for the fractional one. Others use spectral or Galerkin methods. In recent years, the collocation method has also proved to be easy and efficient to implement. Many papers have proved that spectral, Galerkin or collocation methods can be particularly efficient and accurate when special functions are used. Using, for example, the B-spline functions, one can get a multiresolution analysis, i.e., a sequence of nested approximating spaces that cover L²(R). It should be emphasized that the fractional derivative of a B-spline is a fractional B-spline. In this Special Issue, of particular interest are the following subtopics:

• Fractional ordinary differential equations (FODE)
• Fractional partial derivative equations (FPDE)
• Collocation methods
• Galerkin methods
• Spectral methods
• Convergence analysis
• Fractional B-splines

Dr. Laura Pezza
Prof. Dr. Vittoria Bruni
Guest Editors

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