This study establishes the existence and stability of solutions for a general class Riemann–Liouville (RL) fractional differential equations (FDEs) with variable order finite delay. Our findings are confirmed by fixed-point theorems (FPTs) from available literature. We transform RL FDE to alternate integral structure, then use classical FPTs, results studied Hyers–Ulam is established help stand...

The article proposes a nonlocal explicit finite-difference scheme for the numerical solution of nonlinear, ordinary differential equation with derivative fractional variable order Gerasimov–Caputo type. questions approximation, convergence, and stability this are studied. It is shown that conditionally stable converges to first order. Using Riccati as an example, computational accuracy method a...

Fractional differential equations describe nature adequately because of the symmetry properties that physical and biological processes. In this paper, a new approximation is found for variable-order (VO) Riemann–Liouville fractional derivative (RLFD) operator; on basis, an efficient numerical approach formulated VO time-fractional modified subdiffusion (TFMSDE). Complete theoretical analysis pe...

In this paper we present a numerical method for fuzzy differential equation of fractional order under gH-fractional Caputo differentiability. The main idea of this method is to approximate the solution of fuzzy fractional differential equation (FFDE) by an implicit method as corrector and explicit method as predictor. This method is tested on numerical examples.

Using the generalized Kolmogorov-Feller equation with long-range interaction, we obtain kinetic equations with fractional derivatives with respect to coordinates. The method of successive approximations with the averaging with respect to fast variable is used. The main assumption is that the correlator of probability densities of particles to make a step has a power-law dependence. As a result,...