Fractional differential equations : an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications

@inproceedings{Podlubny1999FractionalDE,
  title={Fractional differential equations : an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications},
  author={Igor Podlubny},
  year={1999}
}

Exact and numerical solutions of time-fractional advection–diffusion equation with a nonlinear source term by means of the Lie symmetries

In this paper, the authors analyze a time-fractional advection–diffusion equation, involving the Riemann–Liouville derivative, with a nonlinear source term. They determine the Lie symmetries and

ON L-FRACTIONAL DERIVATIVES AND L-FRACTIONAL HOMOGENEOUS EQUATIONS

Many different fractional derivatives exist that serve different aspects of fractional calculus. Nevertheless, they have failed to correspond to a reliable fractional differential. Lazopoulos [22]

Numerical Solution of Fredholm Fractional Integro-differential Equation with Right-Sided Caputo’s Derivative Using Bernoulli Polynomials Operational Matrix of Fractional Derivative

In this article, fractional integro-differential equation (FIDE) of Fredholm type involving right-sided Caputo’s fractional derivative with multi-fractional orders is considered. Analytical

Hyers-Ulam-Mittag-Leffler stability of fractional differential equations with two caputo derivative using fractional fourier transform

In this paper, we discuss standard approaches to the Hyers-Ulam Mittag Leffler problem of fractional derivatives and nonlinear fractional integrals (simply called nonlinear fractional differential

Generalized Jacobi functions and their applications to fractional differential equations

In this paper, we consider spectral approximation of fractional dif- ferential equations (FDEs). A main ingredient of our approach is to define a new class of generalized Jacobi functions (GJFs),

Caputo–Riesz-Feller fractional wave equation: analytic and approximate solutions and their continuation

In this article a time-space fractional wave equation is studied. In the new proposed fractional model, the second-order time derivative is replaced with a fractional derivative in Caputo sense, and

Caputo–Riesz-Feller fractional wave equation: analytic and approximate solutions and their continuation

In this article a time-space fractional wave equation is studied. In the new proposed fractional model, the second-order time derivative is replaced with a fractional derivative in Caputo sense, and
...