Results 41 to 50 of about 13,452 (220)

Boundary value problem for Caputo-Hadamard fractional differential equations [PDF]

Surveys in Mathematics and its Applications, 2017
The aim of this work is to study the existence and uniqueness solutions for boundary value problem of nonlinear fractional differential equations with Caputo-Hadamard derivative in bounded domain.
Yacine Arioua , Nouredine Benhamidouche
doaj  

Generalized Taylor formulas involving generalized fractional derivatives

, 2017
In this paper, we establish a generalized Taylor expansion of a given function $f$ in the form $\displaystyle{f(x) = \sum_{j=0}^m c_j^{\alpha,\rho}\left(x^\rho-a^\rho\right)^{j\alpha} + e_m(x)}$ \noindent with $m\in \mathbb{N}$, $c_j^{\alpha,\rho}\in
Benjemaa, Mondher
core   +1 more source

A note on Hadamard fractional differential equations with varying coefficients and their applications in probability

, 2017
In this paper we show several connections between special functions arising from generalized COM-Poisson-type statistical distributions and integro-differential equations with varying coefficients involving Hadamard-type operators. New analytical results
Garra, Roberto, Orsingher, Enzo, Polito, Federico   +2 more
core   +1 more source

A generalization of the Lomnitz logarithmic creep law via Hadamard fractional calculus

, 2017
We present a new approach based on linear integro-differential operators with logarithmic kernel related to the Hadamard fractional calculus in order to generalize, by a parameter $\nu \in (0,1]$, the logarithmic creep law known in rheology as Lomnitz ...
Garra, Roberto, Mainardi, Francesco, Spada, Giorgio   +2 more
core   +1 more source

Regional gradient controllability of ultra-slow diffusions involving the Hadamard-Caputo time fractional derivative

, 2019
This paper investigates the regional gradient controllability for ultra-slow diffusion processes governed by the time fractional diffusion systems with a Hadamard-Caputo time fractional derivative.
Cai, Ruiyang, Chen, YangQuan, Ge, Fudong, Kou, Chunhai   +3 more
core   +1 more source

Local density of Caputo-stationary functions in the space of smooth functions [PDF]

, 2016
We consider the Caputo fractional derivative and say that a function is Caputo-stationary if its Caputo derivative is zero. We then prove that any $C^k\big([0,1]\big)$ function can be approximated in $[0,1]$ by a a function that is Caputo-stationary in $[
Bucur, Claudia
core   +2 more sources

Existence and Ulam stability of solutions for Caputo-Hadamard fractional differential equations

General Letters in Mathematics, 2022
In this paper, we study the existence of solutions for fractional differential equations with the Caputo-Hadamard fractional derivative of order α ∈ ( 1,2 ] .
Abduljawad K. Anwar, S. Murad
semanticscholar   +1 more source

The fractional Dodson diffusion equation: a new approach

, 2018
In this paper, after a brief review of the general theory concerning regularized derivatives and integrals of a function with respect to another function, we provide a peculiar fractional generalization of the $(1+1)$-dimensional Dodson's diffusion ...
Garra, Roberto, Giusti, Andrea, Mainardi, Francesco   +2 more
core   +1 more source

The general Caputo–Katugampola fractional derivative and numerical approach for solving the fractional differential equations

Alexandria Engineering Journal
In this manuscript, we present the general fractional derivative (FD) along with its fractional integral (FI), specifically the ψ-Caputo–Katugampola fractional derivative (ψ-CKFD).
Lakhlifa Sadek, Sahar Ahmed ldris, Fahd Jarad   +2 more
doaj   +1 more source

Error estimates of a high order numerical method for solving linear fractional differential equations [PDF]

, 2016
In this paper, we first introduce an alternative proof of the error estimates of the numerical methods for solving linear fractional differential equations proposed in Diethelm [6] where a first-degree compound quadrature formula was used to approximate ...
Adolfsson, Adolfsson, Amblard, Barkai, Diethelm, Diethelm, Diethelm, Diethelm, Elliott, Ervin, Ervin, Ford, Ford, Ford, Ford, Gao, Gao, Gao, Henry, Henry, Jiang, Langlands, Li, Li, Li, Li, Lin, Lin, Liu, Liu, Müller, Neville J. Ford, Podlubny, Scher, Schneider, Sun, Wyss, Yan, Yubin Yan, Zhiqiang Li   +39 more
core   +1 more source