The course will be built around three topics: (1) Prove the almost everywhere equivalence of the L n-th symmetric quantum derivative and the L Peano derivative. (2) Develop a theory of non-linear generalized derivatives, for example of the form ∑ anf(x+ bnh)f(x+ cnh). (3) Classify which generalized derivatives of the form ∑ anf(x + bnh) satisfy the mean value theorem.

The aim of this paper is to establish the existence of solutions of boundary value problems of nonlinear fractional integro-differential equations involving Caputo fractional derivative by using the techniques such as fractional calculus, H"{o}lder inequality, Krasnoselskii's fixed point theorem and nonlinear alternative of Leray-Schauder type. Examples are exhibited to illustrate the main resu...