We prove a new Taylor’s theorem for generalized weighted fractional calculus with nonsingular kernels. The proof is based on the establishment of relations nth-weighted integrals and derivatives. As an application, mean value theorems operators are obtained. Direct corollaries allow one to obtain recent Caputo–Fabrizio, Atangana–Baleanu–Caputo (ABC) ABC

This work investigates the existence and uniqueness of solutions for a coupled system fractional differential equations with three-point generalized integral boundary conditions within proportional derivatives Riemann-Liouville type. By using Schauder Banach fixed point theorems, we study aforesaid system. Finally, present an example to validate our theoretical outcomes.

Using the fact that extremum of variation of generalized action can lead to the fractional dynamics in the case of systems with long-range interaction and long-term memory function, we consider two different applications of the action principle: generalized Noether’s theorem and Hamiltonian type equations. In the first case, we derive conservation laws in the form of continuity equations that c...

We focus on eventually non-linear abstract Cauchy problems with a generalized fractional derivative in time. First we prove local existence and uniqueness result, then Grönwall inequality. Before addressing the inequality, study some properties of eigenvalues eigenfunctions derivatives. Finally, consequences

In this paper, we obtain new generalization of Hermite-Hadamard inequalities via generalized fractional integrals defined by Sarikaya and Ertu?ral in [12]. We establish some midpoint trapezoid type for functions whose first derivatives absolute value are convex involving integrals.

Liouville's fractional integration is used to de ne polygamma functions (z) for negative integer n. It's shown that such (z) can be represented in a closed form by means of the rst derivatives of the Hurwitz Zeta function. Relations to the Barnes G-function and generalized Glaisher's constants are also discussed.