Haar Wavelets Method for Time Fractional Riesz Space Telegraph Equation with Separable Solution. Issue 1 (February 2022)

• Record Type: Journal Article
• Authors: Abdollahy, Z.; Mahmoudi, Y.; Shamloo, A. Salimi; Baghmisheh, M.
• Is Part Of: Reports on mathematical physics. Volume 89:Issue 1(2022)
• Page Start: 81
• Page End: 96
• Publication Date: 2022-02
• Subjects: fractional derivative -- Haar wavelets -- telegraph equation -- Riesz fractional derivative; Mathematical physics -- Periodicals; Physique mathématique -- Périodiques; 530.15
• DOI: 10.1016/S0034-4877(22)00011-8
• Languages: English
• ISSNs: 0034-4877

Abstract

Abstract : In this paper, time fractional Riesz space telegraph partial differential equation is proposed. By applying the variable separation condition, the main telegraph equation, which consists of two variables, is reduced to an ordinary differential equation of single variable. This simplifies the problem computationally. Then the well-known Haar wavelets method is developed to derive the approximate solution of the reduced equation which includes low cost and fast calculations. The error bounds for function approximation are established. To illustrate the reliability and capability of the method, some examples are provided. The results show that the proposed algorithm is very simple and effective.