Related papers: A computationally efficient fractional predictor c…

In this article, we deal with the efficient computation of the Wright function in the cases of interest for the expression of solutions of some fractional differential equations. The proposed algorithm is based on the inversion of the…

We present a general framework for the rigorous numerical analysis of time-fractional nonlinear parabolic partial differential equations, with a fractional derivative of order $\alpha\in(0,1)$ in time. The framework relies on three…

Initial value problem involving Atangana-Baleanu derivative is considered. An Explicit solution of the given problem is obtained by reducing the differential equation to Volterra integral equation of second kind and by using Laplace…

This paper introduces a generalized fractional Halanay-type coupled inequality, which serves as a robust tool for characterizing the asymptotic stability of diverse time fractional functional differential equations, particularly those…

Although the study of functional calculus has already established necessary and sufficient conditions for operators to be fractionalized, this paper aims to use our well-conceived notion of integer powers of operators to construct…

In the paper we deal with linear fractional control problems with constant delays in the state. Single-order systems with fractional derivative in Caputo sense of orders between 0 and 1 are considered. The aim is to introduce a new…

Caputo q-fractional derivatives are introduced and studied. A Caputo -type q-fractional initial value problem is solved and its solution is expressed by means of a new introduced q-Mittag-Leffler function. Some open problems about…

The L-fractional derivative is defined as a certain normalization of the well-known Caputo derivative, so alternative properties hold: smoothness and finite slope at the origin for the solution, velocity units for the vector field, and a…

This paper deals with numerical solutions to a partial differential equation of fractional order. Generally this type of equation describes a transition from anomalous diffusion to transport processes. From a phenomenological point of view,…

Fractional operators (derivatives/integrals) are defined via the integration of the functions. When the function is produced by a spanning set of fractional power functions, traditional quadrature rules often need to be revised, failing to…

Recently, many fractional integral operators were introduced by different mathematicians. One of these fractional operators, Atangana-Baleanu fractional integral operator, was defined by Atangana and Baleanu in [2]. In this study, firstly,…

We investigate the application of a posteriori error estimates to a fractional optimal control problem with pointwise control constraints. Specifically, we address a problem in which the state equation is formulated as an integral form of…

In this paper, we develop a Monte Carlo method for solving PDEs involving an integral fractional Laplacian (IFL) in multiple dimensions. We first construct a new Feynman-Kac representation based on the Green function for the fractional…

In this paper, we study a fast and linearized finite difference method to solve the nonlinear time-fractional wave equation with multi fractional orders. We first propose a discretization to the multi-term Caputo derivative based on the…

The primary goal of this research is to propose a novel architecture for a deep neural network that can solve fractional differential equations accurately. A Gaussian integration rule and a $L_1$ discretization technique are used in the…

General fractional calculus offers an elegant and self-consistent path toward the generalization of fractional calculus to an enhanced class of kernels. Prabhakar's theory can be thought of, to some extent, as an explicit realization of…

It is well-known that the two-parameter Mittag-Leffler (ML) function plays a key role in Fractional Calculus. In this paper, we address the problem of computing this function, when its argument is a square matrix. Effective methods for…

This paper provides a probabilistic approach to solve linear equations involving Caputo and Riemann-Liouville type derivatives. Using the probabilistic interpretation of these operators as the generators of interrupted Feller processes, we…

This paper deals with the kernel-based approximation of a multivariate periodic function by interpolation at the points of an integration lattice -- a setting that, as pointed out by Zeng, Leung, Hickernell (MCQMC2004, 2006) and Zeng,…

Local fractional derivative and integrals are revealed as one of useful tools to deal with everywhere continuous but nowhere differentiable functions in fractal areas ranging from fundamental science to engineering. In this paper, a…