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

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.

Automated summary

This paper introduces a generalization of the squared remainder minimization method for solving multi-term fractional differential equations, with a focus on linear equations. Approximate solutions are considered in terms of linearly independent functions, and the problem is transformed into a minimization problem using the Lagrange-multiplier method. The convergence and theoretical investigation of this approach are discussed, and relevant examples are studied to demonstrate the accuracy of the method and compare the results with other methods.