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In this paper, we present a method for solving national economies in state space with fractional order, we use the triangular function operational matrix of the fractional order integration to solve the fractional-order national economies equation. The method is described and illustrated with numerical simulation. Numerical simulations are given to verify the effectiveness of the proposed method.

In this paper, we propose new technique for solving fractional diffusion-wave equation. This algorithm is based on Triangular Function (TFs) methods, a new fractional operational matrix of integration for the TFs is derived. The TFs and their fractional operational matrix of integration are used to transform the problem under consideration into a linear system of algebraic equations. The new technique is applied to solving two mathematical models. We show that the present approach is relatively easy, efficient and highly accurate.

In this paper we generalize fractional variational problems in [ a , b ] . We allow for the possibility that functions in the space of solution for the optimization problem can blow up at boundary points. The appropriate fractional derivative spaces are introduced and a compact embedding theorem demonstrated. We prove the existence of minimizers for the variational problems which satisfy the Euler–Lagrange equations with Riemann–Liouville boundary conditions. Our method is based on the fractional calculus of variations. An example is given to illustrate the results. [ABSTRACT FROM AUTHOR]

Marine concrete structures such as harbors, ports and bridges are exposed simultaneously to the action of physical and chemical deterioration processes. Deterioration of marine concrete structures and its rehabilitation are challenges of the world of today. Recently, the increasing usage of carbon fiber reinforced polymer (CFRP) composite appears to be a solution for rehabilitation and strengthening of the concrete structures because of its physical and mechanical properties, such as high strength-to-weight ratio, high corrosion /environmental degradation resistance, and easy to handle during construction. In general, rehabilitation of concrete structures is usually done by two types of materials, it is either using cementitious or advanced composite materials. The aim of this paper is to address the issues and challenges of concrete structures in marine environments and strengthening these structures. In the initial part of this paper, an overview of the problems associated with marine environment on concrete structure will be discussed.