On the basis of classical theories, new theories are pioneered by undergoing its inadequacies and widening its scope in many disciplines. Īdvanced development of mathematical theories and techniques has gained very high standard. ![]() After the inception of fuzzy set theory by Zadeh, its attributes have been extended and established to overcome impreciseness of parameters and structures in mathematical modeling, reasoning, and computing. It is the theory of a particular type of interval‐valued functions, in which mapping is made in such a way that it takes all the possible values in and not only the crisp values as found in usual interval‐valued functions. Another wide‐spreading exploration of mathematics is theory of fuzzy calculus, which has a lot of interesting applications in physics, engineering, mechanics, and many others. For these reasons, it is intensively developed and advanced, and existence of its solution is studied by well‐known authors, Euler, Laplace, Liouville, Riemann, Fourier, Abel, Caputo, etc., to further widen its scope in describing various real‐world problems of science, for instance see. The differential models of fractional order, due to the nonlocal properties of fractional operator, are excellent instruments for providing information about the current as well as the historical state of the system. ![]() The characteristic feature of generalizing the classic integer‐order differentiation and n‐fold integration to arbitrary fractional order have broadened its application in modeling several phenomena of physics, mathematics, and engineering. It is worthwhile mentioning, since last few decades, the theory of fractional calculus has gained significant importance in almost every branch of science, for having the capability to consider integrals and derivatives of any arbitrary order.
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