This paper studies a new class of instantaneous and non-instantaneous impulsive boundary value problem involving the generalized ?-Caputo fractional derivative with weight. Depending on critical point theorems some properties ?-Caputo-type integration differentiation, variational construction multiplicity result solutions are established.

Fractional-order calculus is about the differentiation and integration of non-integer orders. Fractional (FC) based on fractional-order thinking (FOT) has been shown to help us understand complex systems better, improve processing signals, enhance control systems, increase performance optimization, even extend enabling potential for creativity. In this article, authors discuss fractional dynami...

in this paper, we prove the existence and uniqueness results to the random fractional functional differential equations under assumptions more general than the lipschitz type condition. moreover, the distance between exact solution and appropriate solution, and the existence extremal solution of the problem is also considered.

The term fractional calculus is more than 300 years old. It is a generalization of the ordinary differentiation and integration to non-integer (arbitrary) order. The subject is as old as the calculus of differentiation and goes back to times when Leibniz, Gauss, and Newton invented this kind of calculation. In a letter to L’Hospital in 1695 Leibniz raised the following question (Miller and Ross...

This paper addresses issues surrounding the concept of fractional quantum mechanics, related to lights propagation in inhomogeneous nonlinear media, specifically restricted a so-called gravitational optics. Besides Schrödinger–Newton equation, we have also concerned with linear and Airy beam accelerations flat curved spaces fractal photonics, Schrödinger where impact Laplacian is discussed. Ano...

the complex-step derivative approximation is applied to compute numerical derivatives. in this study, we propose a new formula of fractional complex-step method utilizing jumarie definition. based on this method, we illustrated an approximate analytic solution for the fractional cauchy-euler equations. application in image denoising is imposed by introducing a new fractional mask depending on s...

We establish the correct solvability of a multipoint nonlocal (in time) problem for evolutionary equation with operator fractional differentiation and an initial function, which is element space generalized functions distribution type. The analytic representation solution presented. also analyze behavior in case unlimited growth time variable (stabilization solution).