this paper presents a rational haar wavelet operational method for solving the inverse laplace transform problemand improves inherent errors from irrational haar wavelet. the approach is thus straightforward, rather simple andsuitable for computer programming. we define that $p$ is the operational matrix for integration of the orthogonalhaar wavelet. simultaneously, simplify the formulaes of li...

Abstract: The object of this study is to develop a self-tuning fractional order proportionalintegral-derivative (SFOPID) controller for controlling the mover position of a direct drive linear voice coil motor (VCM) accurately under different operational conditions. The fractional order proportional-integral-derivative (FOPID) controller can improve the control performances of the conventional i...

in the present paper, a numerical method is considered for solving one-dimensionalheat equation subject to both neumann and dirichlet initial boundaryconditions. this method is a combination of collocation method and radial basis functions (rbfs). the operational matrix of derivative for laguerre-gaussians (lg) radial basis functions is used to reduce the problem to a set of algebraic equations...

in this article, we develop the distributed order fractional hybrid differential equations (dofhdes) with linear perturbations involving the fractional riemann-liouville derivative of order $0 < q < 1$ with respect to a nonnegative density function. furthermore, an existence theorem for the fractional hybrid differential equations of distributed order is proved under the mixed $varphi$-lipschit...

Abstract This paper applies the Heydari–Hosseininia nonsingular fractional derivative for defining a variable-order version of Sobolev equation. The orthonormal shifted discrete Legendre polynomials, as an appropriate family basis functions, are employed to generate operational matrix method this A new related these polynomials is extracted and construct presented method. Using approach, algebr...

In this paper, we first address the general fractional integrals and derivatives with Sonine kernels that possess integrable singularities of power function type at point zero. Both particular cases compositions these operators are discussed. Then proceed a construction an operational calculus Mikusi\'nski for kernels. This is applied analytical treatment some initial value problems differentia...

in this paper, we solve a inhomogeneous fractional klein-gordon equation by the method of separating variables. we apply the method for three boundary conditions, contain dirichlet, neumann, and robin boundary conditions, and solve some examples to illustrate the effectiveness of the method.