Solvability the telegraph equation with purely integral conditions

In this paper a numerical technique is developed for the one-dimensional telegraph equation, we prove the existence, uniqueness, and continuous dependence upon the data of solution to a telegraph equation with purely integral conditions. The proofs are based on a priori estimates and Laplace transform method. Finally, we obtain the solution by using a simple and efficient algorithm for numerical solution.Publisher's Versio

Solvability the telegraph equation with purely integral conditions

In this paper a numerical technique is developed for the one-dimensional telegraph equation. We prove the existence, uniqueness, and continuous dependence upon the data of solution to a telegraph equation with purely integral conditions. The proofs are based on a priori estimates and Laplace transform method. Finally, we obtain the solution by using a simple and efficient algorithm for numerical solution.Publisher's Versio

Existence, uniqueness and numerical solution of a fractional PDE with integral conditions

This paper is devoted to the solution of one-dimensional Fractional Partial Differential Equation (FPDE) with nonlocal integral conditions. These FPDEs have been of considerable interest in the recent literature because fractional-order derivatives and integrals enable the description of the memory and hereditary properties of different substances. Existence and uniqueness of the solution of this FPDE are demonstrated. As for the numerical approach, a Galerkin method based on least squares is considered. The numerical examples illustrate the fast convergence of this technique and show the efficiency of the proposed method

On Theoretical and Numerical Aspect of Fractional Differential Equations with Purely Integral Conditions

In this paper, we are interested in the study of a problem with fractional derivatives having boundary conditions of integral types. The problem represents a Caputo type advection-diffusion equation where the fractional order derivative with respect to time with $1<\alpha <2$. The method of the energy inequalities is used to prove the existence and the uniqueness of solutions of the problem. The finite difference method is also introduced to study the problem numerically in order to find an approximate solution of the considered problem. Some numerical examples are presented to show satisfactory results.Comment: 24 page

Theoretical and numerical aspect of fractional differential equations with purely integral conditions

In this paper, we are interested in the study of a Caputo time fractional advection–diffusion equation with nonhomogeneous boundary conditions of integral types ∫10v(x,t)dx and ∫10xnv(x,t)dx. The existence and uniqueness of the given problem’s solution is proved using the method of the energy inequalities known as the “a priori estimate” method relying on the range density of the operator generated by the considered problem. The approximate solution for this problem with these new kinds of boundary conditions is established by using a combination of the finite difference method and the numerical integration. Finally, we give some numerical tests to illustrate the usefulness of the obtained results

Inversion Laplace transform for integrodifferential parabolic equation with purely nonlocal conditions

In this paper we prove the existence, uniqueness, and continuous dependence upon the data of solution to integrodifferential parabolic equation with purely nonlocal integral conditions. The proofs are based on a priori estimates and Laplace transform method. Finally, we obtain a solution using a numerical technique which is called Stehfest algorithm by inverting the Laplace transform

Existence and Uniqueness for a Solution of Pseudohyperbolic equation with Nonlocal Boundary Condition

Abstract: Motivated by a number of recent investigations, we define and investigate the various properties of a class of pseudohyperbolic equation defined on purely integral (nonlocal) conditions. We derive useful results involving this class including (for example) existence, uniqueness and continuous arising from the Laplace transform method. In addition, we make use of obtaining such a problem to solve the using a numerical technique (Stehfest algorithm) which provides to show the accuracy of the proposed method

On solvability of the integrodifferential hyperbolic equation with purely nonlocal conditions

In this study, we prove the existence, uniqueness, and continuous dependence upon the data of solution to integro-differential hyperbolic equation with purely nonlocal (integral) conditions. The proofs are based on a priori estimates and Laplace transform method. Finally, we obtain the solution using a numerical technique (Stehfest algorithm) by inverting the Laplace transform

Existence and Uniqueness for Multi-Term Sequential Fractional Integro-Differential Equations with Non-Local Boundary Conditions

In this paper we present a new type of non-local multi-point boundary value problems of Caputo type sequential fractional integro-differential equations. The paper shows that existence and uniqueness results can be obtained using standard tools of fixed point theorem. An application to illustrate the power of the obtained results on quantum information theory is discussed