Fractional Order and Fractal Modelling of Electrical Networks

Theoretical and Numerical Aspect of Fractional Differential Equations with Purely Integral Conditions

“…These generalizations play an essential role in engineering, physics and applied mathematics. Due to the properties of Fractional Differential Equations (FDE), different models are created for complex phenomena using FPDEs, for example, in electroanalytical chemistry, viscoelasticity [1,2], porous environment, fluid flow, thermodynamic [3,4], diffusion transport, rheology [5][6][7], electromagnetism, signal processing [8], electrical network [9] and others [10][11][12]. Some relevant applications of fractional differential equations in the modeling of tribo-fatigue systems and new materials can be mentioned as methods for the experimental study of friction in an active system [13], the volumetric damage state of the tribofatigue system in [14], the tribo-fatigue damage transition and mapping for wheel material under rolling-sliding contact condition [15]; this study is based on construction of a tribo-fatigue damage map of high-speed railway wheel material under different tangential forces and contact pressure conditions through JD-1 testing equipment.…”

On Theoretical and Numerical Aspect of Fractional Differential Equations with Purely Integral Conditions

“…Fractional Partial Differential Equations (FPDE) are considered as generalizations of partial differential equations having an arbitrary order and play essential role in engineering, physics and applied mathematics. Due to the properties of Fractional Differential Equations (FDE), the non-local relationships in space and time are used to model a complex phenomena, such as in electroanalytical chemistry, viscoelasticity [10,21], porous environment, fluid flow, thermodynamic [11,34,35], diffusion transport, rheology [5,7,15,26,31,33], electromagnetism, signal processing [20,21,30], electrical network [20] and others [9,13,26,27]. Several problems have been studied in modern physics and technology by using the partial differential equations (PDEs) where the nonlocal conditions were described by integrals, further these integral conditions are of great interest due to their applications in population dynamics, models of blood circulation, chemical engineering thermoelasticity [34].…”