Results 21 to 30 of about 73 (70)

Solvability and Stability of Solutions of (q, τ)‐Fractional Integro‐Differential Models

Journal of Applied Mathematics, Volume 2026, Issue 1, 2026.
In this paper, we investigate a set of nonlinear (q, τ)‐fractional Fredholm integrodifferential equations that involve memory‐type integral kernels and generalized fractional derivatives. Using a Galerkin technique based on (q, τ)‐Legendre polynomials, we designed an approximation solution and provided a numerical scheme for calculating the integral ...
Shaher Momani, Rabha W. Ibrahim, Dumitru Baleanu, Serbay Duran   +3 more
wiley   +1 more source

A Novel Computational Technique for Numerical Approximation of Nonlinear Fractional Dynamical Systems: Convergence and Efficiency Analysis

Journal of Function Spaces, Volume 2026, Issue 1, 2026.
In this work, we study a family of nonlinear fractional dynamical systems and propose a numerical procedure based on the power series iterative method (PSIM). The systems are formulated in terms of the Atangana–Baleanu–Caputo (ABC) fractional derivative, which is well‐suited to the modeling of memory and nonlocal effects.
Faten H. Damag, Amin Saif, Mohammed Alsharafi, Lakhlifa Sadek   +3 more
wiley   +1 more source

A Shifted Third‐Kind Chebyshev Spectral Method for Nonlinear Variable‐Order Fractional Differential Equations

Journal of Function Spaces, Volume 2026, Issue 1, 2026.
This paper presents a spectral collocation method based on shifted Chebyshev polynomials of the third kind (SCP3) for the numerical solution of variable‐order fractional differential equations (VO‐FDEs). The SCP3 basis is employed to construct accurate approximations of the unknown solution over the interval [0, 1], exploiting its orthogonality and ...
Ghadah S. E. Noman, D. D. Pawar, Wenwu Gao   +2 more
wiley   +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

Petrov-Galerkin method for small deflections in fourth-order beam equations in civil engineering

Nonlinear Engineering
This study explores the Petrov–Galerkin method’s application in solving a linear fourth-order ordinary beam equation of the form u″″+qu=fu^{\prime\prime} ^{\prime\prime} +qu=f.
Youssri Youssri Hassan, Atta Ahmed Gamal, Abu Waar Ziad Yousef, Moustafa Mohamed Orabi   +3 more
doaj   +1 more source

A Computational Scheme Based on Fractional Basis Functions For Solving Fractional Bagley–Torvik Equation

Journal of Mathematics, Volume 2025, Issue 1, 2025.
This study aims to present a spectral collocation approach for treating fractional Bagley–Torvik equations using fractional basis functions. The Bagley–Torvik equation is critically important in a wide range of applied scientific and engineering disciplines. The fractional form of the Bagley–Torvik equations enables the modeling of complex systems with
Taghipour M., Aminikhah H., Chang Phang
wiley   +1 more source

Enhancing the accuracy and efficiency of two uniformly convergent numerical solvers for singularly perturbed parabolic convection–diffusion–reaction problems with two small parameters

Demonstratio Mathematica
This study is devoted to designing two hybrid computational algorithms to find approximate solutions for a class of singularly perturbed parabolic convection–diffusion–reaction problems with two small parameters.
Ansari Khursheed J., Izadi Mohammad, Noeiaghdam Samad   +2 more
doaj   +1 more source

Wellposedness and dynamics of two types of reaction–nonlocal diffusion systems under the inhomogeneous spectral fractional Laplacian

Advances in Nonlinear Analysis
Reaction–nonlocal diffusion equations (RNDEs) model nonlocal transport and anomalous diffusion by replacing the Laplacian with a fractional power, capturing diffusion mechanisms beyond Brownian motion.
Yuan Pu, Zegeling Paul A.
doaj   +1 more source

Chaotic and quasi-periodic dynamics in nonlinear micro-strain wave systems: Exact symbolic solutions and symmetry-based analysis

Results in Engineering
This work presents a systematic theoretical and computational investigation of the micro-strain wave (MSW) model, a fundamental nonlinear evolution equation governing propagation phenomena in media with microscale deformation effects.
Mostafa M.A. Khater
doaj   +1 more source

Spectral pricing and Greeks for double-barrier and rebate options via a bordered-banded Chebyshev tau method

Results in Applied Mathematics
We develop and analyse a barrier-aligned Chebyshev integral tau method for pricing double-barrier and rebate options under the Black–Scholes model. The two barriers define the computational corridor exactly, and the interior strike kink of the payoff is ...
Edson Pindza, Claude Rodrigue Bambe Moutsinga   +1 more
doaj   +1 more source