abstract. in this paper, we implement numerical solution of differential equations of frac- tional order based on hybrid functions consisting of block-pulse function and rationalized haar functions. for this purpose, the properties of hybrid of rationalized haar functions are presented. in addition, the operational matrix of the fractional integration is obtained and is utilized to convert compu...

the aim of this paper is to present a new numerical method for solving the bagley-torvik equation. this equation has an important role in fractional calculus. the fractional derivatives are described based on the caputo sense. some properties of the sinc functions required for our subsequentdevelopment are given and are utilized to reduce the computation of solution of the bagley-torvik equatio...

in this paper, first a new homotopy perturbation method for solving a fractional order nonlinear telegraph equation is introduced. by applying the proposed method, the nonlinear equation is translated to linear equations for per iteration of homotopy perturbation method. then, the obtained problems are solved with separation method. in the examples, it is illustrated that the exact solution is ...

This paper studies a new class of instantaneous and non-instantaneous impulsive boundary value problem involving the generalized ?-Caputo fractional derivative with weight. Depending on critical point theorems some properties ?-Caputo-type integration differentiation, variational construction multiplicity result solutions are established.

Szabo's models of acoustic attenuation [Szabo, J. Acoust. Soc. Am. 96(1), 491-500 (1994)] comply well with the empirical frequency power law involving noninteger and odd-integer exponent coefficients while guaranteeing causality, but nevertheless encounter the troublesome issues of hypersingular improper integral and obscurity in implementing initial conditions. The purpose of this paper is to ...

Abstract: In this paper, we are implemented the Chebyshev spectral method for solving the non-linear fractional Klein-Gordon equation (FKGE). The fractional derivative is considered in the Caputo sense. We presented an approximate formula of the fractional derivative. The properties of the Chebyshev polynomials are used to reduce FKGE to the solution of system of ordinary differential equations...

In this paper we investigate optimality conditions for fractional variational problems, with a Lagrangian depending on the Riesz-Caputo derivative. First we prove a generalized Euler-Lagrange equation for the case when the interval of integration of the functional is different from the interval of the fractional derivative. Next we consider integral dynamic constraints on the problem, for sever...

This work is devoted to the study of global solution for initial value problem of interval fractional integrodifferential equations involving Caputo-Fabrizio fractional derivative without singular kernel admitting only the existence of a lower solution or an upper solution. Our method is based on fixed point in partially ordered sets. In this study, we guaranty the existence of special kind of ...

In this article, Ritz approximation have been employed to obtain the numerical solutions of a class of the fractional optimal control problems based on the Caputo fractional derivative. Using polynomial basis functions, we obtain a system of nonlinear algebraic equations. This nonlinear system of equation is solved and the coefficients of basis polynomial are derived. The convergence of the num...

In this study, an effective numerical method for solving fractional differential equations using Chebyshev cardinal functions is presented. The fractional derivative is described in the Caputo sense. An operational matrix of fractional order integration is derived and is utilized to reduce the fractional differential equations to system of algebraic equations. In addition, illustrative examples...