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