Results 61 to 70 of about 16,801 (158)

Stability and convergence analysis of a class of continuous piecewise polynomial approximations for time fractional differential equations

, 2017
We propose and study a class of numerical schemes to approximate time fractional differential equations. The methods are based on the approximation of the Caputo fractional derivative by continuous piecewise polynomials, which is strongly related to the ...
Zegeling, Paul Andries, Zhou, Han
core   +1 more source

Piecewise second kind Chebyshev functions for a class of piecewise fractional nonlinear reaction–diffusion equations with variable coefficients

Alexandria Engineering Journal
In this paper, a new type of piecewise fractional derivative (PFD) is introduced. The ordinary and distributed-order fractional derivatives in the Caputo sense are used to define this type of PFD.
M.H. Heydari, D. Baleanu, M. Bayramu
doaj   +1 more source

A New Variant of B-Spline for the Solution of Modified Fractional Anomalous Subdiffusion Equation

Journal of Function Spaces, 2021
The objective of this paper is to present an efficient numerical technique for solving time fractional modified anomalous subdiffusion equation. Anomalous diffusion equation has its role in various branches of biological sciences. B-spline is a piecewise
M. S. Hashmi, Zainab Shehzad, Asifa Ashraf, Zhiyue Zhang, Yu-Pei Lv, Abdul Ghaffar, Mustafa Inc, Ayman A. Aly   +7 more
doaj   +1 more source

On piecewise-polynomial approximation of functions with a bounded fractional derivative in an L-norm

Journal of Approximation Theory, 1990
The author studies the error in approximating functions with a bounded \((r+\alpha)th\) derivative in an L-norm. Here r is a nonnegative integer, \(\alpha\in [0,1)\), and \(f^{(r+\alpha)}\) is the classical fractional derivative. The author proves that, for any such function f, there exists a piecewise-polynomial of degree s that interpolates f at n ...
openaire   +2 more sources

Stability of solutions to impulsive Caputo fractional differential equations

Electronic Journal of Differential Equations, 2016
Stability of the solutions to a nonlinear impulsive Caputo fractional differential equation is studied using Lyapunov like functions. The derivative of piecewise continuous Lyapunov functions among the nonlinear impulsive Caputo differential equation ...
Ravi Agarwal, Snezhana Hristova, Donal O'Regan   +2 more
doaj  

A Mathematical Model of COVID-19 Using Piecewise Derivative of Fractional Order

European Journal of Pure and Applied Mathematics
Currently the dynamical systems of infectious disease were studied by using various definitions of fractional calculus. Because the mentioned area has the ability to demonstrate the short and long memory terms involve in the physical dynamics of numerous real world problems.
Shabana Naz, Muhammad Sarwar, Kamal Shah, Nahid Fatima, Thabet Abdeljawad   +4 more
openaire   +1 more source

A numerical framework based on piecewise Chebyshev cardinal functions for fractional integro-differential equations

Results in Applied Mathematics
In this study, we develop an operational matrix technique to address a set of fractional nonlinear integro-differential equations with the Caputo–Hadamard derivative. We utilize a family of the piecewise Chebyshev cardinal functions as basis functions in
S. Mansoori Aref, M.H. Heydari, M. Bayram   +2 more
doaj   +1 more source

Existence and Stability Results for Differential Equations with a Variable-Order Generalized Proportional Caputo Fractional Derivative

Mathematics
An initial value problem for a scalar nonlinear differential equation with a variable order for the generalized proportional Caputo fractional derivative is studied. We consider the case of a piecewise constant variable order of the fractional derivative.
Donal O’Regan, Ravi P. Agarwal, Snezhana Hristova, Mohamed I. Abbas   +3 more
doaj   +1 more source

Global attracting solutions to Hilfer fractional differential inclusions of Sobolev type with noninstantaneous impulses and nonlocal conditions

Nonlinear Analysis, 2019
In this paper, we establish the existence of decay mild solutions on an unbounded interval of nonlocal fractional semilinear differential inclusions with noninstantaneous impulses and involving the Hilfer derivative.
JinRong Wang, Ahmed Gamal Ibrahim, Donal O’Regan   +2 more
doaj   +1 more source

Fractional Stochastic Piecewise Approach to Study Hybrid Crossover Dynamics of Corruption Dynamical System: Mathematical and Statistical Analysis with Real Data Simulations

Mathematics
Recently, piecewise differential operators have been introduced to capture crossover dynamics in physical systems. In the evolution of corruption, the underlying dynamics can shift across different regimes.
Laila A. AL-Essa
doaj   +1 more source