Results 41 to 50 of about 38,304 (201)

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

Numerical Methods for Caputo–Hadamard Fractional Differential Equations with Graded and Non-Uniform Meshes

Mathematics, 2021
We consider the predictor-corrector numerical methods for solving Caputo–Hadamard fractional differential equations with the graded meshes logtj=loga+logtNajNr,j=0,1,2,…,N with a≥1 and r≥1, where loga ...
Charles Wing Ho Green, Yanzhi Liu, Yubin Yan   +2 more
semanticscholar   +1 more source

Generalized Hyers–Ulam Stability of Laplace Equation With Neumann Boundary Condition in the Upper Half‐Space

Mathematical Methods in the Applied Sciences, Volume 49, Issue 2, Page 521-530, 30 January 2026.
ABSTRACT This paper investigates the generalized Hyers–Ulam stability of the Laplace equation subject to Neumann boundary conditions in the upper half‐space. Traditionally, Hyers–Ulam stability problems for differential equations are analyzed by examining the system's error, particularly in relation to a forcing term.
Dongseung Kang, Hoewoon B. Kim, Dojin Kim   +2 more
wiley   +1 more source

Multiterm Impulsive Caputo–Hadamard Type Differential Equations of Fractional Variable Order

Axioms, 2022
In this study, we deal with an impulsive boundary value problem (BVP) for differential equations of variable fractional order involving the Caputo–Hadamard fractional derivative.
Amar Benkerrouche, Mohammed Said Souid, Gani Stamov, Ivanka Stamova   +3 more
doaj   +1 more source

Ulam‐type stability of ψ− Hilfer fractional‐order integro‐differential equations with multiple variable delays

Asian Journal of Control, Volume 28, Issue 1, Page 34-45, January 2026.
Abstract We study a nonlinear ψ−$$ \psi - $$ Hilfer fractional‐order delay integro‐differential equation ( ψ−$$ \psi - $$ Hilfer FrODIDE) that incorporates N−$$ N- $$ multiple variable time delays. Utilizing the ψ−$$ \psi - $$ Hilfer fractional derivative ( ψ−$$ \psi - $$ Hilfer‐FrD), we investigate the Ulam–Hyers––Rassias (U–H–R), semi‐Ulam–Hyers ...
Cemil Tunç, Osman Tunç
wiley   +1 more source

Analytical solutions for fractional Navier–Stokes equation using residual power series with $ \mathit{\phi } $-Caputo generalized fractional derivative

AIMS Mathematics
In this study, we aimed to derive analytical solutions for a system of nonlinear time-fractional Navier–Stokes equations in Cartesian coordinates by employing the residual power series method.
Omar Barkat, Awatif Muflih Alqahtani
doaj   +1 more source

New study on Caputo-Hadamard type fractional Neutral Integro-Differential equations [PDF]

Mathematics and Computational Sciences
In this work, we focus on the analysis of fractional-order neutral integro-differential equations using the Caputo-Hadamard fractional derivative. We employed the topological degree method (TDM) to derive results and solutions for these equations.
Emimal Navajothi, Selvi Sellappan
doaj   +1 more source

Extremum principle for the Hadamard derivatives and its application to nonlinear fractional partial differential equations

, 2018
In this paper we obtain new estimates of the Hadamard fractional derivatives of a function at its extreme points. The extremum principle is then applied to show that the initial-boundary-value problem for linear and nonlinear time-fractional diffusion ...
Kirane, Mokhtar, Torebek, Berikbol T.
core   +1 more source

Studies on Fractional Differential Equations With Functional Boundary Condition by Inverse Operators

Mathematical Methods in the Applied Sciences, Volume 48, Issue 11, Page 11161-11170, 30 July 2025.
ABSTRACT Fractional differential equations (FDEs) generalize classical integer‐order calculus to noninteger orders, enabling the modeling of complex phenomena that classical equations cannot fully capture. Their study has become essential across science, engineering, and mathematics due to their unique ability to describe systems with nonlocal ...
Chenkuan Li
wiley   +1 more source