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...

one of the ecient and powerful schemes to solve linear and nonlinear equationsis homotopy analysis method (ham). in this work, we obtain the approximate solution ofa system of partial dierential equations (pdes) by means of ham. for this purpose, wedevelop the concept of ham for a system of pdes as a matrix form. then, we prove theconvergence theorem and apply the proposed method to nd the a...

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:...

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...

New definitions of determinant functionals over the quaternion skew field are given in this paper. The inverse matrix over the quaternion skew field is represented by analogues of the classical adjoint matrix. Cramer rule for right and left quaternionic systems of linear equations have been obtained.