**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**3

# Search results for: Volterra integral equation

##### 3 Spline Collocation for Solving System of Fredholm and Volterra Integral Equations

**Authors:**
N. Ebrahimi,
J. Rashidinia

**Abstract:**

In this paper, numerical solution of system of Fredholm and Volterra integral equations by means of the Spline collocation method is considered. This approximation reduces the system of integral equations to an explicit system of algebraic equations. The solution is collocated by cubic B-spline and the integrand is approximated by the Newton-Cotes formula. The error analysis of proposed numerical method is studied theoretically. The results are compared with the results obtained by other methods to illustrate the accuracy and the implementation of our method.

**Keywords:**
Convergence analysis,
Cubic B-spline,
Newton-
Cotes formula,
System of Fredholm and Volterra integral equations.

##### 2 Stability of Fractional Differential Equation

**Authors:**
Rabha W. Ibrahim

**Abstract:**

We study a Dirichlet boundary value problem for Lane-Emden equation involving two fractional orders. Lane-Emden equation has been widely used to describe a variety of phenomena in physics and astrophysics, including aspects of stellar structure, the thermal history of a spherical cloud of gas, isothermal gas spheres,and thermionic currents. However, ordinary Lane-Emden equation does not provide the correct description of the dynamics for systems in complex media. In order to overcome this problem and describe dynamical processes in a fractalmedium, numerous generalizations of Lane-Emden equation have been proposed. One such generalization replaces the ordinary derivative by a fractional derivative in the Lane-Emden equation. This gives rise to the fractional Lane-Emden equation with a single index. Recently, a new type of Lane-Emden equation with two different fractional orders has been introduced which provides a more flexible model for fractal processes as compared with the usual one characterized by a single index. The contraction mapping principle and Krasnoselskiis fixed point theorem are applied to prove the existence of solutions of the problem in a Banach space. Ulam-Hyers stability for iterative Cauchy fractional differential equation is defined and studied.

**Keywords:**
Fractional calculus,
fractional differential equation,
Lane-Emden equation,
Riemann-Liouville fractional operators,
Volterra integral equation.

##### 1 On One Application of Hybrid Methods For Solving Volterra Integral Equations

**Authors:**
G.Mehdiyeva,
V.Ibrahimov,
M.Imanova

**Abstract:**

**Keywords:**
Volterra integral equation,
hybrid methods,
stability
and degree,
methods of quadrature