Search

In this paper, a numerical method for solving the fractional order Fredholm integrodifferential equations via the Caputo-Liouville derivative is presented. The method uses the wellknown shifted Chebyshev expansion and a truncated series to represent the unknown function. It also incorporates numerical integration techniques like the Trapezoidal, Simpson's 1/3, and Simpson's 8/3 methods. The paper also provides an approximation for the derivative of an integer. The procedure converts the provided problem into a system of algebraic equations using shifted Chebyshev coefficients and collocation points. The coefficients are found by solving this system using well-known techniques like Newton's method. Numerical results are presented graphycally to illustrate the applicability, efficacy, and accuracy of the approach presented in this work. All calculations in this study were performed using the MATHEMATICA software program. [ABSTRACT FROM AUTHOR]

The paper presents error bounds for the second order exponential Runge-Kutta method for parabolic abstract linear time-dependent differential equations incorporating non-smooth initial data. As an example for this particular type of problems, the paper presents a spatial discretization of a partial integro-differential equation arising in financial mathematics, where non-smooth initial conditions occur in option pricing models. For this example, numerical studies of the convergence rate are given. [ABSTRACT FROM AUTHOR]

In this paper, the Volterra-Fredholm integral equation is derived from a linear integrodifferential equation with a fractional order 0 < α < 1 using Riemann--Liouville fractional integral. The existence and uniqueness of the solution are proved using the Picard method. Popular numerical methods; the Toeplitz matrix, and the product Nyström are used in the solution. These methods will prove their effective in solving this type of equation. Two examples are solved using the mentioned methods and the estimation error is calculated. Finally, a comparison between the numerical results is made. [ABSTRACT FROM AUTHOR]

In this paper, the existence and uniqueness of solutions of fractional integro-differential equations with nonlocal boundary conditions is investigated. We establish the existence of solution via Krasnoselskii fixed point theorem; however, the uniqueness results are obtained by applying the contraction mapping principle. [ABSTRACT FROM AUTHOR]

In this paper, the Adomian decomposition method and Modified Technique are successfully applied to find the approximate solutions of the fuzzy system of Volterra integro-differential equations. The approximate solutions obtained have been improved by using the iteration of the integral equation and the numerical solution with the Simpson rule and Trapezoidal rule. These proposed methods gave excellent results close to the exact solution. The results show that the present method is very straightforward and effective. [ABSTRACT FROM AUTHOR]

In this paper, we study a new approach of investigation of existence, uniqueness and stability of the periodic solution of the nonlinear fractional integro-differential equation of type Caputo-Fabrizio fractional derivative with the initial condition, periodic boundary conditions, and integral boundary conditions by using successive approximations method and Banach fixed point theorem. Finally, some examples are present to illustrate the theorems. [ABSTRACT FROM AUTHOR]

In the paper, ideas of the Lomov regularization method are generalized to the Cauchy problem for a singularly perturbed partial integro-differential equation in the case when the integral term contains a rapidly varying kernel. Regularization of the problem is carried out, the normal and unique solvability of general iterative problems is proved. [ABSTRACT FROM AUTHOR]

In this paper we first develop the method of generalized quasilinearization for initial value problem of an integro differential equation and then use it to develop quasilinearization for the periodic boundary value problem of the integro differential equation by using the coupled lower and upper solutions of Type-I. [ABSTRACT FROM AUTHOR]

In this paper, the existence and uniqueness of mild solution for fractional integrodifferential equations with nonlocal initial conditions are investigated by using Hölder's inequality, p--mean continuity and Schauder's fixed point theorem in Banach spaces. The Mittag-Leffler-Ulam stability results are also obtained by using generalized singular Gronwall's inequality. [ABSTRACT FROM AUTHOR]