Recently, impulsive differential equations of arbitrary order under nonlocal conditions together with impulsive conditions have received much attention. Such equations are being increasingly used in modelling of evolution phenomena that are subject to abrupt changes in their states of rest or uniform motion. In addition, many dynamical processes and phenomena can be modelled in a better way via the use of impulsive differential equations under any complex or real order.

In fact, differential operators with fractional order are global in nature and they explain more comprehensively the dynamic processes/phenomena of real-world problems. Significant applications may be found in the modelling of earthquakes, the preservation of a species, sudden fluctuations of economies, absorbent media leakage flow, fluid traffic model dynamics, and under impact mechanical systems, stocking and the heart’s actions. Differential equations of arbitrary order have great importance in the modelling of those dynamical processes and phenomena, which experience unexpected variations. The solutions of such types of differential equations are very interesting and useful for further investigations in the understanding of dynamical phenomena.

This Special Issue will focus on the most recent research and review articles on new methods and techniques to investigate impulsive differential equations of fractional order. Furthermore, studies of various models devoted to physical, chemical, biological processes are welcomed. Additionally, dynamical processes under impulsive conditions, structures, approaches to complex problems with reasonably good accuracy, low and predictable resources are also welcome. Further numerical results to aforesaid problems via using various techniques will also be appreciated. Authors are invited to present theories, algorithms, frameworks, and techniques aimed at studying and investigating impulsive differential equations of fractional order.

Potential topics include but are not limited to the following:

• Iterative techniques for impulsive differential equations
• Solutions of impulsive differential equations via fixed point theory
• Investigation of evolution type impulsive differential equations of fractional order
• Investigation of artificial neural networks and learning systems under impulsive conditions
• Optimizations and stability analysis of biological and physical systems under impulsive conditions
• Hybrid models consisting of impulsive problems of fractional differential equations
• Qualitative analysis of impulsive equations of arbitrary orders
• Topological methods in impulsive differential equations
• Computational methods for fractional PDEs in physics and engineering
• General fractional derivatives involving special functions in signal analysis and image processing
• Fractional impulsive problems in mathematical physics
• Special functions and applications in fractional calculus
• New numerical schemes for nonlinear ordinary differential and integral equations
• New analytical methods for solving ordinary fractional differential and integral equations