Results 81 to 90 of about 582,662 (170)

On Some Impulsive Fractional Integro-Differential Equation with Anti-Periodic Conditions

Fractal and Fractional
We investigate a class of boundary value problems (BVPs) involving an impulsive fractional integro-differential equation (IF-IDE) with the Caputo–Hadamard fractional derivative (C-HFD). We employ some fixed-point theorems (FPTs) to study the existence of
Ymnah Alruwaily, Kuppusamy Venkatachalam, El-sayed El-hady   +2 more
doaj   +1 more source

Spectral approximations to the fractional integral and derivative [PDF]

, 2012
In this paper, the spectral approximations are used to compute the fractional integral and the Caputo derivative. The effective recursive formulae based on the Legendre, Chebyshev and Jacobi polynomials are developed to approximate the fractional ...
Li, Changpin, Liu, Fawang, Fanhai Zeng, Changpin Li, Zeng, Fanhai, Fawang Liu   +5 more
core   +2 more sources

On Averaging Principle for Caputo–Hadamard Fractional Stochastic Differential Pantograph Equation

, 2022
In this paper, we studied an averaging principle for Caputo–Hadamard fractional stochastic differential pantograph equation (FSDPEs) driven by Brownian motion.
Mounia Mouy, Yamina Laskri, Hamid Boulares, Saleh Alshammari, Mohammad Alshammari, Wael W. Mohammed   +5 more
core   +1 more source

Caputo-Type Modification of the Erdélyi-Kober Fractional Derivative [PDF]

, 2007
The Caputo fractional derivative is one of the most used definitions of a fractional derivative along with the Riemann-Liouville and the Grünwald- Letnikov ones.
Luchko, Yury, Trujillo, Juan
core   +1 more source

Convergence analysis of positive solution for Caputo–Hadamard fractional differential equation

Nonlinear Analysis
By deriving the expression of Green function and some of its special properties and establishing appropriate substitution and appropriate cone, the existence of unique iterative positive, error estimation, and convergence rate of approximate solution ...
Limin Guo, Cheng Li, Nan Qiao, Jingbo Zhao   +3 more
doaj   +1 more source

A Discretization of the Hadamard fractional derivative [PDF]

, 2016
We present a new discretization for the Hadamard fractional derivative, that simplifies the computations. We then apply the method to solve a fractional differential equation and a fractional variational problem with dependence on the Hadamard ...
Bastos, Nuno, Almeida, Ricardo
core   +1 more source

Analysis of boundary value problem with multi-point conditions involving Caputo-Hadamard fractional derivative

, 2020
We study the boundary value problems (BVPs) of the Caputo-Hadamard type fractional differential equations (FDEs) supplemented by multi-point conditions.
Muthaiah, Subramanian, Gopal, Thangaraj Nandha   +1 more
core   +1 more source

Fractional Cauchy Problem with Caputo Nabla Derivative on Time Scales [PDF]

, 2015
The definition of Caputo fractional derivative is given and some of its properties are discussed in detail. After then, the existence of the solution and the dependency of the solution upon the initial value for Cauchy type problem with fractional Caputo
Jiang Zhu, Ling Wu
core   +1 more source

Existence and Ulam–Hyers stability results for Caputo–Hadamard fractional differential equations with non-instantaneous impulses

Boundary Value Problems
In this manuscript, we investigated the existence, uniqueness, and Ulam–Hyers stability results of solutions to implicit Caputo–Hadamard fractional differential equations with noninstantaneous impulses and δ − d e r i v a t i v e $\delta -derivative ...
Mesfin Teshome Beyene, Mitiku Daba Firdi, Tamirat Temesgen Dufera   +2 more
doaj   +1 more source

High Order Approximation to Caputo Derivative On Graded Mesh and Time-Fractional Diffusion Equation for Non-smooth Solutions

In this paper, a high-order approximation to Caputo-type time-fractional diffusion equations involving an initial-time singularity of the solution is proposed.
Kumari, Shweta, Singh, Abhishek Kumar, Mehandiratta, Vaibhav, Mehra, Mani   +3 more
core   +1 more source