‎In recent years‎, ‎many methods have been studied for solving differential equations of fractional order‎, ‎such as Lie group method, ‎invariant subspace method and numerical methods‎, ‎cite{6,5,7,8}‎. Among this‎, ‎the method of characteristics is an efficient and practical method for solving linear fractional differential equations (FDEs) of multi-order‎. In this paper we apply this method f...

The current paper contributes a novel framework for solving a class of linear matrix differential equations. To do so, the operational matrix of the derivative based on the shifted Bernoulli polynomials together with the collocation method are exploited to reduce the main problem to system of linear matrix equations. An error estimation of presented method is provided. Numerical experiments are...

The index of matrix A in Cn.n is equivalent to the dimension of largest Jor-dan block corresponding to the zero eigenvalue of A. In this paper, indicialequations and normal equations for solving inconsistent singular linear systemof equations are investigated.

The main purpose of this paper is to consider Adomian's decomposition method in non-linear Volterra integro-differential equations. The advantages of this method, compared with the recent numerical techniques (in particular the implicitly linear collocation methods) , and the convergence of Adomian's method applied to such nonlinear integro-differential equations are discussed. Finally, by ...

Varying methods exist for computing a presentation of a finitely generated commutative cancellative monoid.We use an algorithm of Contejean andDevie [An efficient incremental algorithm for solving systems of linear diophantine equations, Inform. andComput. 113 (1994) 143–172] to show how these presentations can be obtained from the nonnegative integer solutions to a linear system of equations. ...

This article clarifies what it means to solve a system of fuzzy linear equations, relying on the fact that they are a direct extension of interval linear systems of equations, already studied in a specific interval mathematics literature. We highlight four distinct definitions of a systems of linear equations where coefficients are replaced by intervals, each of which based on a generalization ...

Several decompositions of, symmetric matrices for calculating inertia and solving systems of linear equations are discussed. New partial pivoting strategies for decomposing symmetric matrices are introduced and analyzed.

1. Overview: 4/1/13 1 2. First-Order Linear Differential Equations: 4/3/13 2 3. Examples of Integrating Factors: 4/5/13 4 4. Separation of Variables: 4/8/13 5 5. Autonomous Equations: 4/10/13 7 6. Exact Equations: 4/12/13 9 7. More Exact Equations: 4/15/13 10 8. Numerical Methods and Existence and Uniqueness: 4/17/13 11 9. Review of Weeks 1 to 3: 4/19/13 12 10. Systems of Differential Equation:...

fractional calculus has been used to model the physical and engineering processes that have found to be best described by fractional differential equations. for that reason, we need a reliable and efficient technique for the solution of fractional differential equations. the aim of this paper is to present an analytical approximation solution for linear and nonlinear multi-order fractional diff...

Let a⊕b = max(a, b) and a⊗b = a+b for a, b ∈ R and extend the pair of operations to matrices and vectors in the same way as in linear algebra. The homogeneous twosided system in max-algebra is of the form A⊗ x = B ⊗ x. No polynomial method for solving homogeneous system is known. In this paper, we consider homogeneous twosided linear systems in max-algebra in a special case. We show that it can...