Nontrivial solutions for a fractional advection dispersion equation in anomalous diffusion

Approximate Controllability for Functional Equations with Riemann-Liouville Derivative by Iterative and Approximate Method

“…In recent years, a considerable interest has been paid to functional evolution equations with fractional derivatives since they are of importance in describing the natural phenomenon including the models in stochastic processes, finance, and physics (see [1][2][3][4][5][6][7][8][9]). On the other hand, the notion of controllability plays a central role in the study of the theory of control and optimization.…”

New Result on the Critical Exponent for Solution of an Ordinary Fractional Differential Problem

“…Traditionally, for the transport of solute in nonheterogeneous porous media, based on the conservation principle and Ficks law, we can use the integer-order differential equation to describe the whole convection-diffusion process. However, it has been established that the convection diffusion equation based on Ficks law fails to model the anomalous feature of diffusion in porous media, and thus fractional order convectiondiffusion equations have the potential to accurately model the convection-diffusion process [6][7][8][9][10]. On the other hand, fractional order integral and derivative operators are nonlocal which can describe the behaviour of many complex processes and systems with long-memory in time.…”

Infinitely many solutions for a class of p-Laplacian equation with Sturm-Liouville type nonhomogeneous boundary conditions

“…In the last decade or so, as a useful method to obtain the existence or multiplicity results, Ricceri's Variational Principle has been extended and used widely to study many problems including: Kirchhoff-type problems ( [1,12,15,19,20,26]), problems with impulsive effect ( [6,11,21,29]), fractional differential equations ( [27,32]), p-Laplacian or p(x)-Laplacian equations ( [2-4, 13, 14, 16]), Yamabe equations ( [9]), superlinear discrete problems ( [8]), non-differential functionals ( [5,7,22]), and many other problems (see [17,25,30] and the references therein).…”