Results 31 to 40 of about 1,380 (204)

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

Perturbed functional fractional differential equation of Caputo-Hadamard order [PDF]

Mathematica Moravica
In this paper, we investigate the existence of solution and extremal solutions for an initial-value problem of perturbed functional fractional differential equations with Caputo-Hadamard derivative.
Hamani Samira
doaj   +1 more source

Existence of Solutions for a Coupled System of p-Laplacian Caputo–Hadamard Fractional Sturm–Liouville–Langevin Equations with Antiperiodic Boundary Conditions

Journal of Mathematics, 2022
Fractional Sturm–Liouville and Langevin equations have recently attracted much attention. In this paper, we investigate a coupled system of fractional Sturm–Liouville–Langevin equations with antiperiodic boundary conditions in the framework of Caputo ...
Jinbo Ni, Jifeng Zhang, Wei Zhang
doaj   +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

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

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

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

A Review of Certain Modern Special Functions and Their Applications

Abstract and Applied Analysis, Volume 2026, Issue 1, 2026.
This review article comprehensively analyzes recent developments in the generalization of special functions (SFs) and polynomials via various fractional calculus operators (FCOs), focusing on the analytical properties and applications of extended Hurwitz–Lerch zeta, Wright, and hypergeometric functions.
Hala Abd Elmageed, Mohamed Abdalla, AbdelMaksoud Soliman   +2 more
wiley   +1 more source

Jacobi polynomials method for a coupled system of Hadamard fractional Klein–Gordon–Schrödinger equations

Alexandria Engineering Journal
In this work, the Caputo-type Hadamard fractional derivative is utilized to introduce a coupled system of time fractional Klein–Gordon-Schrödinger equations.
M.H. Heydari, M. Razzaghi
doaj   +1 more source

Mellin Transforms of the Generalized Fractional Integrals and Derivatives

, 2014
We obtain the Mellin transforms of the generalized fractional integrals and derivatives that generalize the Riemann-Liouville and the Hadamard fractional integrals and derivatives.
Bucchianico, Butkovskii, Butzer, Butzer, Butzer, Butzer, Bóna, Erdélyi, Erdélyi, Flajolet, Gaboury, Goldman, Hadamard, Herrmann, Katugampola, Katugampola, Kilbas, Kilbas, Kilbas, Kilbas, Kiryakova, Machado, Miller, Noor, Noor, Noor, Odzijewicz, Odzijewicz, Odzijewicz, Oldham, Podlubny, Pooseh, Robbins, Robinson, Rodrigues, Roman, Roman, Roman, Rota, Rota, Samko, Udita N. Katugampola, Yakubovich   +42 more
core   +1 more source