Generalized squared remainder minimization method for solving multi-term fractional differential equations

• Main Authors: Mir Sajjad Hashemi, Mustafa Inc, Somayeh Hajikhah
• Format: Article
• Language: English
• Published: Vilnius University Press 2021-01-01
• Series: Nonlinear Analysis
• Subjects: squared remainder minimization method; Lagrange-multiplier method; multi-term fractional differential equation
• Online Access: https://www.journals.vu.lt/nonlinear-analysis/article/view/20560
• ISSN: 1392-5113; 2335-8963

In this paper, we introduce a generalization of the squared remainder minimization method for solving multi-term fractional differential equations. We restrict our attention to linear equations. Approximate solutions of these equations are considered in terms of linearly independent functions. We change our problem into a minimization problem. Finally, the Lagrange-multiplier method is used to minimize the resultant problem. The convergence of this approach is discussed and theoretically investigated. Some relevant examples are investigated to illustrate the accuracy of the method, and obtained results are compared with other methods to show the power of applied method.