Results 41 to 50 of about 615,518 (166)

Composition of Fractional Integral and Derivative Operators: Summarised in Tables

Mathematical Methods in the Applied Sciences, Volume 49, Issue 13, Page 14682-14696, 15 September 2026.
ABSTRACT This paper compiles a complete, detailed list of composition properties for Riemann–Liouville fractional differintegrals, in all possible cases for orders anywhere in the complex plane, with the results presented clearly in a table for easy visual consumption.
Arran Fernandez
wiley   +1 more source

Uncertainty Quantification of Analytical Solutions for the Nonlinear Space and Time Fractional Order ϕ4$$ {\phi}^4 $$ Equation Under Fuzziness

Engineering Reports, Volume 8, Issue 7, July 2026.
Analytical fuzzy soliton solutions of a modified space–time fractional ϕ4$$ {\phi}^4 $$ model are derived using EHFM, capturing memory effects and uncertainty. Results reveal diverse wave structures and show how fractional order and fuzziness significantly influence soliton amplitude, localization, and propagation, with heightened sensitivity near the ...
Mohsin Khalid, Neha Andaleeb Khalid, Baboucarr Ceesay, Zafar Iqbal   +3 more
wiley   +1 more source

Combination Synchronization of Fractional Systems Involving the Caputo–Hadamard Derivative

Mathematics, 2021
The main aim of this paper is to investigate the combination synchronization phenomena of various fractional-order systems using the scaling matrix. For this purpose, the combination synchronization is performed by considering two drive systems and one ...
Abdelhameed M. Nagy, Abdellatif Ben Makhlouf, Abdulaziz Alsenafi, Fares Alazemi   +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

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

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

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

A singularity-inferred operator-consistent fractional PINN for one- and two-dimensional third-kind Caputo–Hadamard auto-convolution Volterra equations with weakly singular kernels

Results in Engineering
We propose a singularity-inferred operator-consistent fractional physics-informed neural network for one- and two-dimensional third-kind Caputo–Hadamard auto-convolution Volterra equations with weakly singular kernels.
Essaid Aourir, Hojatollah Laeli Dastjerdi, Kamal Shah, Thabet Abdeljawad   +3 more
doaj   +1 more source

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

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