Impulsive fractional differential equations with nonlinear boundary conditions

Impulsive Problems for Fractional Differential Equations with Functional Boundary Value Conditions at Resonance

“…Fractional differential equations have proved valuable and effective tools in the modeling of many phenomena in various fields of biology, medicine, mechanics, engineering, viscoelasticity, and so forth; see [4,5]. In order to improve the mathematical modeling of several concepts arising in these areas, many researchers have paid a considerable attention to the subject of impulsive fractional differential equations in the recent literature [6][7][8][9][10][11][12][13].…”

On impulsive sequential fractional differential equations with separated boundary conditions

“…These attentions can be attributed to widely-used of fractional differential equations tools in many scientific fields such as chemistry, biology, physics, control theory, viscoelasticity, electrochemistry, signal processing, nuclear dynamics, etc; see [[1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13]]. In fact, both Sequential Fractional Differential Equations (SFDEs), and Impulsive Fractional Differential Equations (IFDEs), have received a great deal of attention from many authors see [ [14], [15], [16], [17]]. However, a new topic has been investigated by combining both SFDEs and IFDEs, which in turn produced ISFDEs to be a much wider case.…”

Stability of a class of nonlinear fractional order impulsive switched systems

“…They have great applications in nonlinear oscillations of earthquakes, many physical phenomena such as seepage flow in porous media and in the fluid dynamic traffic model. Applications and analysis of fractional order differential equations in different areas were considered by many authors and some basic results on fractional order differential equations have been obtained; see for example, Cao and Chen (2012), Feckan et al (2012), Hilfer (2000), Mainardi (1997), Ahmad and Nieto (2011) and Podlubny (1999). Actually, fractional order differential equations are considered as an alternative model to integer differential equations.…”