a computational method for numerical solution of a nonlinear volterra and fredholm integro-differentialequations of fractional order based on chebyshev cardinal functions is introduced. the chebyshev cardinaloperational matrix of fractional derivative is derived and used to transform the main equation to a system ofalgebraic equations. some examples are included to demonstrate the validity and ...

the purpose of this paper is to study the fuzzy fractional differentialequations. we prove that fuzzy fractional differential equation isequivalent to the fuzzy integral equation and then using this equivalenceexistence and uniqueness result is establish. fuzzy derivative is considerin the goetschel-voxman sense and fractional derivative is consider in theriemann liouville sense. at the end, we...

Model generation has emergcd as a key task in engineering design and analysis. Al research in this area has focusedon model based reasoning emphasising qualitative models in attempting to automate this process. In this paper, we propose that this work on the use of model based reasoning in model generation would benefit from the inclusion of case-based reasoning (CBR) techniques. We argue that ...

with x0 ∈ R, B ∈ R and E,A ∈ R, such that the pencil sE − A ∈ R[s] is regular, that is, det(sE −A) 6= 0. For systems governed by ordinary differentialequations (that is, E is the identity matrix), a rigorous analysis of this problem has its origin in the 60s of the 20th century [6, 8–10, 13, 15, 21]. In particular, the article [20] by Willems gives a complete characterization of linear-quadrati...

In this paper, an elastic shell model is presented for postbuckling prediction of a long thinwalledcylindrical shell under axial compression. The Ritz method is applied to solve the governingequilibrium equation of a cylindrical shell model based on the von-Karman type nonlinear differentialequations. The postbuckling equilibrium path is obtained using the energy method for a long thin-walledcy...

in this paper, we investigate the canonical property of solutions of a system of differentialequations having a singularity and turning point of even order. first, by a replacement, we transform thesystem to the sturm-liouville equation with a turning point. using the asymptotic estimates for a specialfundamental system of solutions of sturm-liouville equation, we study the infinite product rep...

Adaptive moving spatial meshes are useful for solving physical models given by time-dependent partial differentialequations. However, special consideration must be when combining adaptive meshing procedures with ensemble-based data assimilation (DA) techniques. In particular, we focus on the case where each ensemble member evolvesindependently upon its own mesh and is interpolated to a common D...

A two dimensional two-delays differential system modeling the dynamics of stem-like cells and white-blood cells in Chronic Myelogenous Leukemia under treatment is considered. Stability of equilibria is investigated and emergence of periodic solutions of limit cycle type, as a result of a Hopf bifurcation, is eventually shown. All three types of stem cell division (asymmetric division, symmetric...

The unsteady free convection flow between two long vertical parallel plates withvariable temperature and mass diffusion in the presence of the thermal radiation hasbeen presented. The governing dimensionless coupled linear partial differentialequations on the flow are solved by using the Laplace transform technique. TheExact solutions have been obtained for the fluid velocity, temperature and t...

The fuzzy set theory introduced by Zadeh has emerged as an interesting and fascinating branch of pure and applied sciences. The applications of fuzzy set theory can be found in many branches of regional, physical, mathematical, differential equations andengineering sciences. Recently, the authors have made important research results in the theory of fuzzy differentialequations, integrodifferent...