University of Isfahan Mathematics and Society 2345-6493 2 4 2018 02 20 Fractional calculus: from theory to applications Fractional calculus: from theory to applications 59 69 22116 10.22108/msci.2017.100109.1201 FA Journal Article 2016 11 14 This article introduces fractional calculus, including the definition of fractional derivatives and integrals, as well as the governing relationships, similarities, and differences between fractional calculus and classical calculus. We also delve into the geometric interpretation of fractional derivatives and integrals. Furthermore, we present applications of fractional calculus and fractional differential equations. This article introduces fractional calculus, including the definition of fractional derivatives and integrals, as well as the governing relationships, similarities, and differences between fractional calculus and classical calculus. We also delve into the geometric interpretation of fractional derivatives and integrals. Furthermore, we present applications of fractional calculus and fractional differential equations. https://math-sci.ui.ac.ir/article_22116_1d2a4fb6a28b2eaa6da67aecd48af4ef.pdf