Results 71 to 80 of about 13,452 (220)

An Infinite System of Fractional Order with p-Laplacian Operator in a Tempered Sequence Space via Measure of Noncompactness Technique

Fractal and Fractional, 2021
In the current study, a new class of an infinite system of two distinct fractional orders with p-Laplacian operator is presented. Our mathematical model is introduced with the Caputo–Katugampola fractional derivative which is considered a generalization ...
Ahmed Salem, Lamya Almaghamsi, Faris Alzahrani   +2 more
doaj   +1 more source

Application of (q, τ)‐Bernoulli Interpolation to the Spectral Solution of Quantum Differential Equations

International Journal of Differential Equations, Volume 2025, Issue 1, 2025.
In order to solve fractional differential equations on quantum domains, this work provides a spectral approach based on higher‐order (q, τ)‐Bernoulli functions and polynomials. We build a robust basis for approximation in (q, τ)‐weighted Hilbert spaces by using the orthogonality properties of these extended polynomials and the Sheffer‐type generating ...
Shaher Momani, Rabha W. Ibrahim, Khalil Ezzinbi   +2 more
wiley   +1 more source

Simultaneous determination of a source term and diffusion concentration for a multi-term space-time fractional diffusion equation

Mathematical Modelling and Analysis, 2021
An inverse problem of determining a time dependent source term along with diffusion/temperature concentration from a non-local over-specified condition for a space-time fractional diffusion equation is considered.
Salman A. Malik, Asim Ilyas, Arifa Samreen   +2 more
doaj   +1 more source

Solvability of Implicit Fractional Systems With Nonlocal Conditions in Weighted Functional Spaces

International Journal of Differential Equations, Volume 2025, Issue 1, 2025.
This paper investigates the existence and uniqueness of solutions for a class of nonlinear implicit Riemann–Liouville fractional integro‐differential equations subject to nonlocal conditions in a weighted Banach space. The inclusion of both implicit effects and nonlocal terms introduces additional complexity, making the analysis both challenging and ...
Abdulrahman A. Sharif, Maha M. Hamood, Kirtiwant P. Ghadle, Sining Zheng   +3 more
wiley   +1 more source

Approximate Solutions for the Differential Equations by Using the Nonconformable Fractional Sumudu Transform

International Journal of Mathematics and Mathematical Sciences, Volume 2025, Issue 1, 2025.
This research introduces the nonconformable fractional Sumudu transform (NCFST) methodology. We used the above strategy to solve fractional differential equations (FDEs) via nonconformable fractional derivatives (NCFDs). We examined and demonstrated its fundamental qualities and benefits.
Shams A. Ahmed, Mohammed G. S. Al-Safi, Tarig M. Elzaki, Shikha Binwal   +3 more
wiley   +1 more source

Approximations for Fractional Derivatives and Fractional Integrals Using Padé Approximation

Journal of Applied Mathematics, Volume 2025, Issue 1, 2025.
This paper tackles the persistent challenge of slow convergence and numerical instability in the fractional calculus when applied to power series–representable functions fx=∑i=0∞cixi, limitations that compromise accuracy in scientific applications. A novel reformulation of fractional derivatives and integrals is achieved by applying Padé approximation ...
Ahmed M. Youssef, Tamer M. Rageh, Aisha F. Fareed, M. S. Abdelwahed, Manzoor Hussain   +4 more
wiley   +1 more source

Inverse Problems of Determining Sources of the Fractional Partial Differential Equations

, 2019
In this chapter, we mainly review theoretical results on inverse source problems for diffusion equations with the Caputo time-fractional derivatives of order $\alpha\in(0,1)$. Our survey covers the following types of inverse problems: 1. determination of
Li, Zhiyuan, Liu, Yikan, Yamamoto, Masahiro   +2 more
core   +1 more source

Innovative observer design for nonlinear systems using Caputo fractional derivative with respect to another function

AIMS Mathematics
This work introduces a novel control framework using the Caputo fractional derivative (CFD) with respect to another function—a derivative that has not been thoroughly treated in control theory.
Kareem Alanazi, Omar Naifar, Raouf Fakhfakh, Abdellatif Ben Makhlouf   +3 more
doaj   +1 more source

Fractional isoperimetric Noether's theorem in the Riemann-Liouville sense

, 2013
We prove Noether-type theorems for fractional isoperimetric variational problems with Riemann-Liouville derivatives. Both Lagrangian and Hamiltonian formulations are obtained. Illustrative examples, in the fractional context of the calculus of variations,
Almeida, Almeida, Atanacković, Atanacković, Baleanu, Bartosiewicz, Chen, Delfim F.M. Torres, El-Nabulsi, Ferreira, Frederico, Frederico, Frederico, Frederico, Gastão S.F. Frederico, Gelfand, Herzallah, Hilfer, Jafari, Kilbas, Kiryakova, Kiryakova, Klimek, Leitmann, Malinowska, Malinowska, Malinowska, Martins, Odzijewicz, Odzijewicz, Podlubny, Pooseh, Pooseh, Riewe, Riewe, Torres, Torres, Torres, Torres, van Brunt   +39 more
core   +1 more source

Existence and Stability Results for a Modified Diffusion Equation Involving Atangana–Baleanu–Caputo Fractional Derivative

Journal of Applied Mathematics, Volume 2025, Issue 1, 2025.
This article shows another display of the modified diffusion equation of fractional order involving Atangana–Baleanu–Caputo fractional derivative. The manuscript contains three major cases: the existence of a solution, uniqueness of the solution, and Hyers–Ulam stability, which are discussed based on valid theorems in nonlinear analysis.
Maral Sangi, Mohammad Esmael Samei, Arpan Hazra   +2 more
wiley   +1 more source