Results 1 to 10 of about 1,485,427 (242)
Solving Helmholtz Equation with Local Fractional Derivative Operators [PDF]
Fractal and Fractional, 2019 The paper presents a new analytical method called the local fractional Laplace variational iteration method (LFLVIM), which is a combination of the local fractional Laplace transform (LFLT) and the local fractional variational iteration method (LFVIM ...
Dumitru Baleanu +2 more
doaj +5 more sources
A robust approach for computing solutions of fractional-order two-dimensional Helmholtz equation [PDF]
Scientific ReportsThe Helmholtz equation plays a crucial role in the study of wave propagation, underwater acoustics, and the behavior of waves in the ocean environment. The Helmholtz equation is also used to describe propagation through ocean waves, such as sound waves ...
Muhammad Nadeem +3 more
doaj +4 more sources
Exact Solutions of the 3D Fractional Helmholtz Equation by Fractional Differential Transform Method
Journal of Function Spaces, 2022 In this work, we applied the fractional reduced differential transform method (FRDTM) to find the exact solutions of the three-dimensional fractional Helmholtz equation (FHE) and compared our outcomes with the tenth-order approximate solutions for ...
Saleh Alshammari, Salah Abuasad
doaj +4 more sources
On convergence analysis and numerical solutions of local fractional Helmholtz equation
Alexandria Engineering Journal, 2020 Local fractional q-homotopy analysis transform method (q -HATM) is employed to solve the local fractional Helmholtz equation. Uniqueness and convergence analysis of the method is investigated by Banach’s fixed point theory. Solutions are expressed in the
Luu Vu Cam Hoan +4 more
doaj +5 more sources
A Modification Fractional Homotopy Perturbation Method for Solving Helmholtz and Coupled Helmholtz Equations on Cantor Sets [PDF]
Fractal and Fractional, 2019 In this paper, we apply a new technique, namely, the local fractional Laplace homotopy perturbation method (LFLHPM), on Helmholtz and coupled Helmholtz equations to obtain analytical approximate solutions.
Dumitru Baleanu, Hassan Kamil Jassim
doaj +4 more sources
A Fast Solver for the Fractional Helmholtz Equation
SIAM Journal of Scientific Computing, 2021 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Chester Weiss +2 more
exaly +5 more sources
Novel Evaluation of Fuzzy Fractional Helmholtz Equations
Journal of Function Spaces, 2022 The current article discusses the fuzzy new iterative transform approach, which is a combination of a fuzzy hybrid methodology and an iterative transformation technique. We establish the consistence of our strategy by obtaining fractional fuzzy Helmholtz
Meshari Alesemi +2 more
doaj +3 more sources
On the Relationship between the Inhomogeneous Wave and Helmholtz Equations in a Fractional Setting
Abstract and Applied Analysis, 2019 We study convergence of solutions of a space and time inhomogeneous fractional wave equation on the quarter-plane to the stationary regime described by solutions of the Helmholtz equation.
Mateo Dulce, Alexander Getmanenko
doaj +4 more sources
Partial Differential Equations in Applied MathematicsThis work investigates the dynamics of optical waves to the generalized coupled nonlinear fractional Helmholtz equation with quintic and cubic nonlinear effects.
Naila Nasreen +3 more
doaj +3 more sources
Complex and Real Valued Solutions for Fractional Helmholtz Equation
Mathematical Methods in the Applied SciencesABSTRACTIn this paper, we are concerned with the limiting absorption principle for the fractional Helmholtz equation: , where and are two real parameters. By establishing the boundedness estimate for the resolvent of fractional Helmholtz operator, we obtain the nontrivial complex valued solutions for the fractional Helmholtz equation. By setting
Zifei Shen
exaly +3 more sources