University of TabrizComputational Methods for Differential Equations2345-39828120200101A Shifted Chebyshev-Tau method for finding a time-dependent heat source in heat equation113945010.22034/cmde.2019.9450ENSamanehAkbarpourDepartment of Mathematics, Lahijan Branch,
Islamic Azad University, Lahijan, Iran.AbdollahShidfarDepartment of Mathematics, Lahijan Branch,
Islamic Azad University, Lahijan, Iran.HashemSaberinajafiDepartment of Mathematics, Lahijan Branch,
Islamic Azad University, Lahijan, Iran.0000-0001-6723-8126Journal Article20180420This paper investigates the inverse problem of determining the time-dependent 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.<br /> https://cmde.tabrizu.ac.ir/article_9450_316d610f8aa0b862c298dff9ad145fab.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39828120200101Oscillatory behavior for nonlinear delay differential equation with several non-monotone arguments1427947010.22034/cmde.2019.9470ENÖzkanÖkalanAkdeniz University, Faculty of Science
Department of Mathematics, 07058
Antalya, Turkey.NurtenKılıçDumlupınar University, Faculty of Science and Arts Department of Mathematics, 43000
Kütahya, TurkeyUmutÖzkanAfyon Kocatepe University, Faculty of Science and Arts Department of Mathematics, ANS Campus, 03200
Afyon, TurkeySerminÖztürkAfyon Kocatepe University, Faculty of Science and Arts Department of Mathematics, ANS Campus, 03200
Afyon, TurkeyJournal Article20180402This 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.<br /> https://cmde.tabrizu.ac.ir/article_9470_055c88970bf87985ee592f5aac540b53.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39828120200101New extended direct algebraic method for the Tzitzica type evolution equations arising in nonlinear optics2853947210.22034/cmde.2019.9472ENSeyed MehdiMirhosseini-AlizaminiDepartment of Mathematics, Payame Noor University (PNU), P.O. Box 19395-3697, Tehran, IranHadiRezazadehFaculty of Engineering Technology, Amol University of Special Modern Technologiesl, Amol, Iran0000-0003-3800-8406MostafaEslamiDepartment of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran.0000-0001-6168-7916MohammadMirzazadehDepartment of Engineering Sciences, Faculty of Technology and Engineering, East of Guilan, University of Guilan, Rudsar-Vajargah, Iran.AlpertKorkmazDepartment of Mathematics,
Cankiri Karatekin University, Cankiri, Turkey.Journal Article20180429In 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 Dodd-Bullough-Mikhailor 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.https://cmde.tabrizu.ac.ir/article_9472_62cac0c46c957af29dce04d05abe9ef8.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39828120200101Neumann method for solving conformable fractional Volterra integral equations5468949810.22034/cmde.2019.9498ENMousaIlieDepartment of Mathematics, Rasht Branch, Islamic Azad University, Rasht, Iran0000-0002-1165-8815JafarBiazarDepartment of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, P.O. Box. 41335-1914, Guilan, Rasht, IranZainabAyatiDepartment of Engineering sciences, Faculty of Technology and Engineering East of Guilan, University of Guilan P.C.44891-Rudsar-Vajargah,Iran0000-0001-5854-1051Journal Article20180222This paper deals with the solution of a class of Volterra integral equations in the sense of the conformable fractional derivative. For this goal, the well-organized 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.https://cmde.tabrizu.ac.ir/article_9498_12684e63120212de6f16ee8af2cdab4a.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39828120200101Stress intensity factor for multiple cracks in an infinite plate using hypersingular integral equations69849461ENRaziehGhorbanpoorDepartment of Applied Mathematics, Ferdowsi University of Mashhad, Mash-
had, IranJafarSaberi_NadjafiDepartment of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad,
Iran.Nik Mohd AssriNik LongDepartment of Mathematics, Universiti Putra Malaysia, 43400 Serdang, Selangor, MalaysiaMajidErfanianDepartment of Science, School of Mathematical Sciences, University of Zabol,
Zabol, Iran0000-0001-8449-9272Journal Article20180118In 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.https://cmde.tabrizu.ac.ir/article_9461_c56282baf626de200a29d0039e2453c9.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39828120200101Self-adjointness, conservation laws and invariant solutions of the Buckmaster equation8598946310.22034/cmde.2019.9463ENSaeedeRashidiFaculty of mathematical sciences, Shahrood university of technology,
Shahrood, Semnan, Iran.Seyed RezaHejaziFaculty of mathematical sciences, Shahrood university of technology,
Shahrood, Semnan, Iran.Journal Article20180221The 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 non-linear self-adjointness 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.<br /> https://cmde.tabrizu.ac.ir/article_9463_f78862000f96b1af77f85835ebfa8af1.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39828120200101Legendre-collocation spectral solver for variable-order fractional functional differential equations99110946510.22034/cmde.2019.9465ENRamy MahmoudHafezDepartment of Mathematics, Faculty of Education, Matrouh University, Egypt.0000-0001-9533-3171Youssri HassanYoussriDepartment of Mathematics, Faculty of Science, Cairo University, Giza-EgyptJournal Article20180524A numerical method for the variable-order fractional functional differential equations (VO-FFDEs) 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 Gauss-Legendre nodes were then utilized to reduce the VO-FFDEs 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.https://cmde.tabrizu.ac.ir/article_9465_7bf2db00ba7908179a8ab1d172df790f.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39828120200101Approximate nonclassical symmetries for the time-fractional KdV equations with the small parameter111118946810.22034/cmde.2019.9468ENRaminNajafiDepartment of Mathematics,
Maku Branch, Islamic Azad University,
Maku, Iran0000-0003-2432-2947Journal Article20180902In this paper, the Lie symmetry analysis is presented for the time-fractional KdV equation with the Riemann-Liouville 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.https://cmde.tabrizu.ac.ir/article_9468_51ba4ecfd1b0bde07487daac3911aafc.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39828120200101K-fractional integral inequalities of Hadamard type for (h − m)−convex functions119140946210.22034/cmde.2019.9462ENGhulamFarid1
COMSATS University Islamabad, Attock CampusAtiq UrRehmanCOMSATS University Islamabad, Attock Campus, Kamra road, Attock 43600, PakistanQurat UlAinCOMSATS University Islamabad, Attock Campus, Kamra road, Attock 43600, PakistanJournal Article20180911In 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 Riemann-Liouville (RL) k-fractional integrals: a generalization of RL fractional integrals. Several known results are special cases of proved results.https://cmde.tabrizu.ac.ir/article_9462_090c2defb846ad8871f5652fa0bde183.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39828120200101Impulsive initial value problems for a class of implicit fractional differential equations141154945510.22034/cmde.2019.9455ENAmjad S.ShaikhDepartment of Mathematics, AKI's Poona College of Arts, Science and Commerce,
Camp, Pune, India0000-0003-4829-1698Bhausaheb R.SontakkeDepartment of Mathematics, Pratishthan Mahavidyalaya, Paithan, Dist. Aurangabad, IndiaJournal Article20180927In 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.https://cmde.tabrizu.ac.ir/article_9455_c809eb601105b6b16deefc7e7664ae68.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39828120200101Meshless local radial point interpolation (MLRPI) to two dimensional wave equation with Neumann’s boundary conditions155172946410.22034/cmde.2019.9464ENElyasShivanianDepartment of Applied Mathematics, Imam Khomeini International University, Qazvin, 34149-16818, IranMostafaHosseiniDepartment of Applied Mathematics, Imam Khomeini International University, Qazvin, 34149-16818, IranAsgharRahimiDepartment of Applied Mathematics, Imam Khomeini International University, Qazvin, 34149-16818, IranJournal Article20180506In 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 two-step time discretization method with the help of Crank-Nicolson technique is employed to approximate the time derivatives. Convergence studies in the numerical example show that MLRPI method possesses excellent rates of convergence.https://cmde.tabrizu.ac.ir/article_9464_2436e78017e3fbb60ea238e23b3c4f75.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39828120200101A Study on Functional Fractional Integro-Differential Equations of Hammerstein type173193962110.22034/cmde.2019.9621ENLeilaSaeediDepartment of Mathematics,
Shahed University, Tehran, Iran.AbolfazlTari MarzabadDepartment of Mathematics,
Shahed University, Tehran, Iran.EsmailBabolianDepartment of Computer Science, Kharazmi University, Tehran, Iran.Journal Article20181009In this paper, functional Hammerstein integro-differential 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.https://cmde.tabrizu.ac.ir/article_9621_f7a4fd4fee54f1eab443d316c79e5488.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39828120200101A new method for constructing exact solutions for a time-fractional differential equation194204952510.22034/cmde.2019.9525ENElhamLashkarianFaculty of Mathematical Sciences,
Shahrood University of Technology,
Shahrood, Semnan, Iran.Seyed RezaHejaziFaculty of Mathematical Sciences,
Shahrood University of Technology,
Shahrood, Semnan, Iran.NooraHabibiFaculty of Mathematical Sciences,
Shahrood University of Technology,
Shahrood, Semnan, Iran.0000-0001-7106-1052Journal Article20171225In 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.https://cmde.tabrizu.ac.ir/article_9525_7cf852901c4f7baaf3405d8e8947bf45.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39828120200101The solving integro-differential equations of fractional order with the ultraspherical functions205211965510.22034/cmde.2019.9655ENAliKhaniFaculty of Sciences, Department of Mathematics, Azarbaijan Shahid Madani
University, Tabriz, Iran0000000289284235SaeidPanahyFacutly of Sciences Department of Mathematical , Azarbaijan Shahid Madani University, Tabriz, IranJournal Article20181016In this paper, an integration method is presented based on using ultraspherical polynomials for solving a class of linear fractional integro-di_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 higher-order derivatives. Numerical example illustrate the efficiency and accuracy of the method.https://cmde.tabrizu.ac.ir/article_9655_4fadc94c41f9800d90c3f50c47193d78.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39828120200101Algorithm for solving the Cauchy problem for stationary systems of fractional order linear ordinary differential equations212221952610.22034/cmde.2019.9526ENFikretAlievInstitute of Applied Mathematics, Baku State University, Z.Khalilov str, 23, AZ1148, Baku AzerbaijanNihanAlievInstitute of Applied Mathematics, Baku State University, Z.Khalilov str, 23, AZ1148, Baku AzerbaijanNargizSafarovaInstitute of Applied Mathematics, Baku State University, Z.Khalilov str, 23, AZ1148, Baku AzerbaijanNailaVelievaInstitute of Applied Mathematics, Baku State University, Z.Khalilov str, 23, AZ1148, Baku AzerbaijanJournal Article20190719A 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.https://cmde.tabrizu.ac.ir/article_9526_34e7ba013b67fb9e9218892109264c08.pdf