Nonlinear grey system models, serving to time series forecasting, are extensively used in diverse areas of science and engineering. However, most research concerns improving classical models developing novel relatively limited attention has been paid the relationship among modelling mechanism. The current paper proposes a unified framework reconstructs model from an integro-differential equatio...

Frequency-dependent attenuation typically obeys an empirical power law with an exponent ranging from 0 to 2. The standard time-domain partial differential equation models can describe merely two extreme cases of frequency-independent and frequency-squared dependent attenuations. The otherwise nonzero and nonsquare frequency dependency occurring in many cases of practical interest is thus often ...

In this paper, we propose an efficient numerical method for solving initial boundary value problem a coupled system of equations consisting nonlinear parabolic partial integro-differential equation and elliptic with term. This has important applied significance in petroleum engineering finds application modeling two-phase nonequilibrium fluid flows porous medium generalized law. The constructio...

We discuss the approximate controllability of nonlinear fractional integro-differential system under the assumptions that the corresponding linear system is approximately controllable. Using the fixed-point technique, fractional calculus and methods of controllability theory, a new set of sufficient conditions for approximate controllability of fractional integro-differential equations are form...