TY  - JOUR
A1  - Roul, Pradip
T1  - Numerical solutions of time fractional degenerate parabolic equations by variational iteration method with Jumarie-modified Riemann-Liouville derivative
JF  - Mathematical methods in the applied sciences
N2  - In this article, the fractional variational iteration method is employed for computing the approximate analytical solutions of degenerate parabolic equations with fractional time derivative. The time-fractional derivatives are described by the use of a new approach, the so-called Jumarie modified Riemann-Liouville derivative, instead in the sense of Caputo. The approximate solutions of our model problem are calculated in the form of convergent series with easily computable components. Moreover, the numerical solution is compared with the exact solution and the quantitative estimate of accuracy is obtained. The results of the study reveal that the proposed method with modified fractional Riemann-Liouville derivatives is efficient, accurate, and convenient for solving the fractional partial differential equations in multi-dimensional spaces without using any linearization, perturbation or restrictive assumptions.
KW  - variational iteration method
KW  - biological population equations
KW  - fractional calculus
KW  - exact solution
KW  - Mittag-Leffler function
Y1  - 2011
U6  - https://doi.org/10.1002/mma.1418
SN  - 0170-4214
VL  - 34
IS  - 9
SP  - 1025
EP  - 1035
PB  - Wiley-Blackwell
CY  - Malden
ER  - 
TY  - JOUR
A1  - Sandev, Trifce
A1  - Tomovski, Zivorad
A1  - Dubbeldam, Johan L. A.
A1  - Chechkin, Aleksei V.
T1  - Generalized diffusion-wave equation with memory kernel
JF  - Journal of physics : A, Mathematical and theoretical
N2  - We study generalized diffusion-wave equation in which the second order time derivative is replaced by an integro-differential operator. It yields time fractional and distributed order time fractional diffusion-wave equations as particular cases. We consider different memory kernels of the integro-differential operator, derive corresponding fundamental solutions, specify the conditions of their non-negativity and calculate the mean squared displacement for all cases. In particular, we introduce and study generalized diffusion-wave equations with a regularized Prabhakar derivative of single and distributed orders. The equations considered can be used for modeling the broad spectrum of anomalous diffusion processes and various transitions between different diffusion regimes.
KW  - diffusion-wave equation
KW  - Mittag-Leffler function
KW  - anomalous diffusion
Y1  - 2018
U6  - https://doi.org/10.1088/1751-8121/aaefa3
SN  - 1751-8113
SN  - 1751-8121
VL  - 52
IS  - 1
PB  - IOP Publ. Ltd.
CY  - Bristol
ER  -