Fractional calculus

Fractional calculus is a branch of mathematical analysis that studies the several different possibilities of defining real number powers or complex number powers of the differentiation operator Dwhere in the last step we exchanged the order of integration and pulled out the f (s) factor from the t integration. Changing variables to r defined by t = s + (x − s)r, Fractional calculus is a branch of mathematical analysis that studies the several different possibilities of defining real number powers or complex number powers of the differentiation operator D and of the integration operator J and developing a calculus for such operators generalizing the classical one. In this context, the term powers refers to iterative application of a linear operator D to a function f, that is, repeatedly composing D with itself, as in D 2 ( f ) = ( D ∘ D ) ( f ) = D ( D ( f ) ) {displaystyle D^{2}(f)=(Dcirc D)(f)=D(D(f))} .