Department of Electronics, University of Kashmir,
Srinagar, Jammu and Kashmir, India
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Fractional calculus which is the basically the generalization of integer-order calculus, has a history of about 300 years. However, owing to its computational complexity and lack of intuitive physical and geometric explanations, it failed to attract the interest of researchers in its earlier stages. Recently, fractional calculus has been proven to be a valuable tool in the modeling of many applications in physics, electronic circuits, bio-materials, and electrochemistry and the researchers have discovered that using fractional calculus to describe many natural phenomena will be more accurate, such as biomedical engineering, fractional control, and speciﬁc physical problems. Recently, many generalized (fractional-order) theorems have been introduced from which existing conventional theorems arise as special cases. As a generalized case the application of the fundamentals of fractional calculus into many of the physics problems, engineering applications showing the advantages of the resulting systems compared to conventional integer-order systems, has been the priority for many of the researchers recently. Extensive research activity in this area has been on-going as more potential real-world applications are highlighted and investigated. In recent years, the research of artificial neural networks based on fractional calculus has attracted much attention. A lot of work in this field can be seen in the open literature. It has been seen that the fraction-order implementation is resulting in mimicking the natural neural networks to the greater extend compared to their integer-order counterpart. Furthermore, the fractional calculus model is considered as an excellent tool to describe the hereditary and memory characteristics of various processes due to a memory term in the model, which is proving to be one of the key factors in the modeling of the neural networks.