Green–Haar wavelets method for generalized fractional differential equations
Copyright policy )Green–Haar wavelets method for generalized fractional differential equations
AbstractThe objective of this paper is to present two numerical techniques for solving generalized fractional differential equations. We develop Haar wavelets operational matrices to approximate the solution of generalized Caputo–Katugampola fractional differential equations. Moreover, we introduce Green–Haar approach for a family of generalized fractional boundary value problems and compare the method with the classical Haar wavelets technique. In the context of error analysis, an upper bound for error is established to show the convergence of the method. Results of numerical experiments have been documented in a tabular and graphical format to elaborate the accuracy and efficiency of addressed methods. Further, we conclude that accuracy-wise Green–Haar approach is better than the conventional Haar wavelets approach as it takes less computational time compared to the Haar wavelet method.
- University of the Sciences United States
- Prince Sultan University Saudi Arabia
- National University of Science and Technology Oman
- National University of Sciences and Technology Pakistan
- Çankaya University Turkey
Artificial intelligence, Fractional Differential Equations, Economics, generalized fractional differential equations, Fractional ordinary differential equations, Wavelets, Caputo-Katugampola derivative, wavelets, Theory and Applications of Fractional Differential Equations, Mathematical analysis, Generalized fractional differential equations, Context (archaeology), Differential equation, Fractional derivatives and integrals, Numerical Methods for Singularly Perturbed Problems, Numerical methods for wavelets, QA1-939, FOS: Mathematics, Boundary value problem, Biology, Anomalous Diffusion Modeling and Analysis, Economic growth, Numerical Analysis, Applied Mathematics, Haar, Haar wavelet, Paleontology, Partial differential equation, Applied mathematics, Computer science, Fractional Derivatives, Modeling and Simulation, Caputo–Katugampola derivative, Physical Sciences, Convergence (economics), Discrete wavelet transform, Wavelet transform, Wavelet, Mathematics, Ordinary differential equation
Artificial intelligence, Fractional Differential Equations, Economics, generalized fractional differential equations, Fractional ordinary differential equations, Wavelets, Caputo-Katugampola derivative, wavelets, Theory and Applications of Fractional Differential Equations, Mathematical analysis, Generalized fractional differential equations, Context (archaeology), Differential equation, Fractional derivatives and integrals, Numerical Methods for Singularly Perturbed Problems, Numerical methods for wavelets, QA1-939, FOS: Mathematics, Boundary value problem, Biology, Anomalous Diffusion Modeling and Analysis, Economic growth, Numerical Analysis, Applied Mathematics, Haar, Haar wavelet, Paleontology, Partial differential equation, Applied mathematics, Computer science, Fractional Derivatives, Modeling and Simulation, Caputo–Katugampola derivative, Physical Sciences, Convergence (economics), Discrete wavelet transform, Wavelet transform, Wavelet, Mathematics, Ordinary differential equation
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).31 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 10% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Top 10%
Citations provided by BIP!Popularity provided by BIP!