Non-local fractional derivatives are generally more effective in mimicking real-world phenomena and offer precise representations of physical entities, such as the oscillation earthquakes behavior polymers. This study aims to solve 2D fractional-order diffusion-wave equation using Riemann–Liouville time-fractional derivative. The is solved modified implicit approach based on integral sense. the...

In this work, numerical solution of multi term space fractional PDE is calculated by using radial basis functions. The derivatives functions are evaluated Caputo and Riemann-Liouville definitions. Local applied to get stable accurate the problem. Accuracy method assessed double mesh procedure. Numerical solutions presented for different orders show effect introducing fractionality.

The problem of finding Lie point symmetries for a certain class multi-dimensional nonlinear partial fractional differential equations and their systems is studied. It assumed that considered involve derivatives with respect to only one independent variable, each equation contains single derivative. most significant examples such are time-fractional models processes memory power-law type. Two di...

‎In this paper‎, ‎we consider a new study about fractional $Delta$-difference equations‎. ‎We consider two special classes of Sturm-Liouville problems equipped with fractional $Delta$-difference operators‎. ‎In couple of steps‎, ‎the Lyapunov type inequalities for both classes will be obtained‎. ‎As application‎, ‎some qualitative behaviour of mentioned fractional problems such as stability‎, ‎...

*Correspondence: [email protected] Department of Mathematics and Physical Sciences, Prince Sultan University, P.O. Box 66833, Riyadh, 11586, Saudi Arabia Abstract In this article, we extend fractional calculus with nonsingular exponential kernels, initiated recently by Caputo and Fabrizio, to higher order. The extension is given to both left and right fractional derivatives and integrals. ...

In this paper, a class of fractional advection-dispersion models (FADMs) is considered. These models include five fractional advection-dispersion models, i.e., the times FADM, the mobile/immobile time FADM with a time Caputo fractional derivative 0 < γ < 1, the space FADM with two sides Riemann-Liouville derivatives, the timespace FADM and the time fractional advection-diffusion-wave model with...

We consider the fractional generalizations of Liouville equation. The normalization condition, phase volume, and average values are generalized for fractional case. The interpretation of fractional analog of phase space as a space with fractal dimension and as a space with fractional measure are discussed. The fractional analogs of the Hamiltonian systems are considered as a special class of no...