فهرست مطالب
 Volume:8 Issue: 1, 2020
 تاریخ انتشار: 1398/10/11
 تعداد عناوین: 15


Pages 113This paper investigates the inverse problem of determining the timedependent heat source and the temperature for the heat equation with Dirichlet boundary conditions and an integral over determination conditions. The numerical method is presented for solving the Inverse problem. Shifted Chebyshev polynomial is used to approximate the solution of the equation as a base of the tau method which is based on the Chebyshev operational matrices. The main advantage of this method is based upon reducing the partial differential equation into a system of algebraic equations of the solution. Numerical results are presented and discussed.Keywords: Inverse source problem, Heat equation, Shifted Chebyshev polynomial, Operational matrix, Shifted ChebyshevTau method

Pages 1427This paper is devoted to obtaining some new sufficient conditions for the oscillation of all solutions of first order nonlinear differential equations with several deviating arguments. Finally, an illustrative example related to our results is given.Keywords: Nonlinear, Delay differential equation, Nonmonotone argument, Oscillatory solutions, Nonoscillatory solutions

Pages 2853
In this study, the new extended direct algebraic method is exerted for constructing more general exact solutions of the three nonlinear evolution equations with physical interest namely, the Tzitzeica equation, the DoddBulloughMikhailor equation and the Liouville equation. By using of an appropriate traveling wave transformation reduces these equations to ODE. We state that this method is excellently a generalized form to obtain solitary wave solutions of the nonlinear evolution equations that are widely used in theoretical physics. The method appears to be easier and faster by means of symbolic computation system.
Keywords: Nonlinear evolution equation, Tzitzica type evolution equations, New extended direct algebraic method, traveling wave solutions 
Pages 5468This paper deals with the solution of a class of Volterra integral equations in the sense of the conformable fractional derivative. For this goal, the wellorganized Neumann method is developed and some theorems related to existence, uniqueness, and sufficient condition of convergence are presented. Some illustrative examples are provided to demonstrate the efficiency of the method in solving conformable fractional Volterra integral equations.Keywords: Volterra integral equations, Conformable fractional derivative, Neumann method, Existence, uniqueness, sufficient condition of convergence

Pages 6984
In this paper, numerical solutions of multiple cracks problems in an infinite plate are studied. Hypersingular integral equations (hieq) for the cracks are formulated using the complex potential method. For all kernels such as regular or hypersingular kernels, we are using the appropriate quadrature formulas to solve and evaluate the unknown functions numerically. Furthermore, by using this equation the stress intensity factor (SIF) was calculated for crack tips. For two serial cracks (horizontal) and two dissimilar cracks (horizontal and inclined), our numerical results agree with the previous works.
Keywords: Hypersingular integral equation, Multiple cracks problem, Inclined cracks, Double stress intensity factors 
Pages 8598
The present paper considers the group analysis of extended (1 + 1)dimensional Buckmaster equation and its conservation laws. Symmetry operators of Buckmaster equation are found via Lie algorithm of differential equations. The method of nonlinear selfadjointness is applied to the considered equation. The infinite set of conservation laws associated with the finite algebra of Lie point symmetries of the Buckmaster equation is computed. The corresponding conserved quantities are obtained from their respective densities. Furthermore, the similarity reductions corresponding to the symmetries of the equation are constructed.
Keywords: Buckmaster equation, Lie point symmetry, Direct method, Homotopy operator, Similarity Reductions 
Legendrecollocation spectral solver for variableorder fractional functional differential equationsPages 99110A numerical method for the variableorder fractional functional differential equations (VOFFDEs) has been developed. This method is based on approximation with shifted Legendre polynomials. The properties of the latter were stated, first. These properties, together with the shifted GaussLegendre nodes were then utilized to reduce the VOFFDEs into a solution of matrix equation. Sequentially, the error estimation of the proposed method was investigated. The validity and efficiency of our method were examined and verified via numerical examples.Keywords: Variableorder fractional functional differential equations, Shifted Legendre polynomials, GaussLegendre nodes, Matrix equation

Pages 111118In this paper, the Lie symmetry analysis is presented for the timefractional KdV equation with the RiemannLiouville derivative. We introduce a generalized approximate nonclassical method that is applied to differential equations with fractional order. In the sense of this symmetry, the vector fields of fractional KdV equation are obtained. The similarity reduction corresponding to the symmetries of the equation is constructed.Keywords: Approximate Lie symmetry analysis, Timefractional KdV equation, Groupinvariant solution

Pages 119140In this paper, we establish Hadamard type fractional integral inequalities for a more general class of functions that is the class of (h _ m)_convex functions. These results are due to RiemannLiouville (RL) kfractional integrals: a generalization of RL fractional integrals. Several known results are special cases of proved results.Keywords: RiemannLiouville fractional integrals, RiemannLiouville k−fractional integrals, (h − m)−convex functions

Pages 141154In this article we consider, impulsive initial value problems for a class of implicit fractional differential equations involving the Caputo fractional derivative of order β in (1,2]. The solutions of this nonlinear equation are analyzed by establishing sufficient conditions for existence and uniqueness using Banach's contraction mapping principle and the Schaefer's fixed point theorem. In addition, using the Banach contraction principle, we establish uniqueness result. To demonstrate main results two examples are presented.Keywords: Initial value problem, Implicit fractional differential equations, Impulses, fixed point theorem

Pages 155172In this article, the meshless local radial point interpolation (MLRPI) methods are applied to simulate two dimensional wave equation subject to given appropriate initial and Neumann’s boundary conditions. In MLRPI method, all integrations are carried out locally over small quadrature domains of regular shapes such as square or circle. The radial point interpolation method is proposed to construct shape functions for MLRPI. A weak formulation with a Heaviside step function transforms the set of governing equations into local integral equations on local sub domains where Neumann’s boundary condition is imposed naturally. A twostep time discretization method with the help of CrankNicolson technique is employed to approximate the time derivatives. Convergence studies in the numerical example show that MLRPI method possesses excellent rates of convergence.Keywords: Meshless local radial point interpolation (MLRPI), Local weak formulation, Radial basis function, 2D wave equation, Neumann’s boundary conditions, Finite difference

Pages 173193In this paper, functional Hammerstein integrodifferential equations of fractional order is studied. Here the existence and uniqueness of the solution is proved. A numerical method to approximate the solution of problem is also presented which is based on an improvement of the successive approximations method. Error estimation of the method is analyzed and error bound is obtained. The convergence and stability of the method are proved. At the end, application of the method is revealed by presenting some examples.Keywords: Functional Hammerstein integrodifferential equations, Fractional order, Successive approximations, Spline interpolation, Trapezoidal quadrature rule

Pages 194204
In the present paper the process of finding new solutions from previous solutions of a given fractional differential equation (FDE) is considered. For this issue, first we should construct an exact solution by using the symmetry operators of the equation. Then, the commutator brackets of the obtained operators give new solutions from old ones via a systematic method.
Keywords: Lie point symmetry, fractional calculus, fractional differential equation, Exact solution 
Pages 205211In this paper, an integration method is presented based on using ultraspherical polynomials for solving a class of linear fractional integrodi_erential equations of Volterra types. This method is based on a new investigation of ultrasphreical integration to approximate the highest order derivative in the equations and generate approximations to the lower order derivatives through integration of the higherorder derivatives. Numerical example illustrate the efficiency and accuracy of the method.Keywords: Fractional integrodifferential equation, Ultraspherical functions, Caputo derivative

Pages 212221A new simplified analytical formula is given for solving the Cauchy problem for a homogeneous system of fractional order linear differential equations with constant coefficients (SFOLDECC). The matrix exponential function in this formula is re placed by a Taylor series. Next, an analytical expression of the integral is obtained, with the help of which, for the transition matrix, a relation is obtained that allows one to obtain a solution of the Cauchy problem with high accuracy. The results also apply to the case of inhomogeneous systems with constant perturbations and are illustrated by numerical examples.Keywords: Cauchy problem, Linear fractional derivative system, MittagLeffler function, Constant matrix coefficients