Results 51 to 60 of about 582,712 (204)

Recovering the space source term for the fractional-diffusion equation with Caputo–Fabrizio derivative

Journal of Inequalities and Applications, 2021
This article is devoted to the study of the source function for the Caputo–Fabrizio time fractional diffusion equation. This new definition of the fractional derivative has no singularity. In other words, the new derivative has a smooth kernel.
Le Nhat Huynh, Nguyen Hoang Luc, Dumitru Baleanu, Le Dinh Long   +3 more
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

Refinements of some fractional integral inequalities involving extended convex functions and fractional Caputo derivatives

Journal of Inequalities and Applications
This article examines famous fractional Hermite–Hadamard integral inequalities through the applications of fractional Caputo derivatives and extended convex functions. We develop modifications involving two known classical fractional extended versions of
Muhammad Imran, Shahid Mubeen, Aziz Khan, Thabet Abdeljawad   +3 more
doaj   +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

New Fractional Integral Inequalities for Convex Functions Pertaining to Caputo–Fabrizio Operator

Fractal and Fractional, 2022
In this article, a generalized midpoint-type Hermite–Hadamard inequality and Pachpatte-type inequality via a new fractional integral operator associated with the Caputo–Fabrizio derivative are presented.
Soubhagya Kumar Sahoo, Pshtiwan Othman Mohammed, Bibhakar Kodamasingh, Muhammad Tariq, Y. S. Hamed   +4 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

Nonlinear boundary value problems for fractional differential inclusions with Caputo-Hadamard derivatives on the half line

AIMS Mathematics, 2021
The authors establish sufficient conditions for the existence of solutions to a boundary value problem for fractional differential inclusions involving the Caputo-Hadamard type derivative of order $ r \in (1, 2] $ on infinite intervals. Both cases of convex and nonconvex valued right hand sides are considered.
Mouffak Benchohra, John R. Graef, Nassim Guerraiche, Samira Hamani   +3 more
openaire   +2 more sources

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

Applications of Fixed Point Theory to Investigate a System of Fractional Order Differential Equations

Journal of Function Spaces, 2021
We investigate a nonlinear system of pantograph-type fractional differential equations (FDEs) via Caputo-Hadamard derivative (CHD). We establish the conditions for existence theory and Ulam-Hyers-type stability for the underlying boundary value system ...
Zareen A. Khan, Israr Ahmad, Kamal Shah
doaj   +1 more source

Numerical Investigation of Fractional Third‐Order Differential Equation Using Quartic B‐Spline Functions

Advances in Mathematical Physics, Volume 2026, Issue 1, 2026.
Fractional calculus (FC) has become more popular during the past four decades due to its extensive applications in mathematics, physics, engineering, and statistics. B‐spline functions offer flexible and incredibly precise approximations because of their piecewise polynomial structure and smoothness at knots.
Syeda Alishba Batool, Muhammad Abbas, Madiha Shafiq, Y. S. Hamed, Asnake Birhanu, Ivan Giorgio   +5 more
wiley   +1 more source