# 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} }

## 4,133 Citations

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

- Mathematics
- 2018

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

- Mathematics
- 2017

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

- MathematicsMediterranean Journal of Mathematics
- 2019

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

- MathematicsAIMS Mathematics
- 2021

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

- MathematicsMath. Comput.
- 2016

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

- MathematicsJournal of Applied Mathematics and Computing
- 2018

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

- Mathematics
- 2019

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…