The Legendre wavelet method for solving fractional differential equations

In this research, a Bernoulli wavelet operational matrix of fractional integration is presented Bernoulli wavelets and their properties are employed for deriving a general procedure for forming this matrix The application of the proposed operational matrix for solving the fractional delay differential equations is explained Also, upper bound for the error of operational matrix of the fractional integration is given This operational matrix is utilized to transform the problem to a set of algebraic equations with unknown Bernoulli wavelet coefficients Several numerical examples are solved to demonstrate the validity and applicability of the presented technique

A new operational matrix based on Bernoulli wavelets for solving fractional delay differential equations

Numerical solution of fractional pantograph differential equations by using generalized fractional-order Bernoulli wavelet

Control of a novel class of fractional-order chaotic systems via adaptive sliding mode control approach ☆

On Haar wavelet operational matrix of general order and its application for the numerical solution of fractional Bagley Torvik equation

Haar wavelet operational matrix of fractional order integration and its applications in solving the fractional order differential equations

Fractional-order systems, because of its long-memory nature. have been used increasingly to model natural phenomena. However, Computational difficulties of the fractional-order calculus have delayed application of fractional-order systems in engineering. For this purpose, after deriving the fractional-order integral matrix of the Haar wavelet we present a method for analysis of the fractional-order systems. Examples verify the correctness and feasibility of the proposed method. The method greatly facilate the design of fractional-order control systems.

Haar wavelet-based simulation of the fractional-order systems

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Haar wavelet operational matrix of fractional order integration and its applications in solving the fractional order differential equations

Haar wavelet-based simulation of the fractional-order systems