Generalized squared remainder minimization method for solving multi-term fractional differential equations
Articles
Mir Sajjad Hashemi
University of Bonab
https://orcid.org/0000-0002-5529-3125
Mustafa Inc
Firat University
https://orcid.org/0000-0003-4996-8373
Somayeh Hajikhah
University of Bonab
Published 2021-01-01
https://doi.org/10.15388/namc.2021.26.20560
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Keywords

squared remainder minimization method
Lagrange-multiplier method
multi-term fractional differential equation

How to Cite

Hashemi M. S., Inc M. and Hajikhah S. (2021) “Generalized squared remainder minimization method for solving multi-term fractional differential equations”, Nonlinear Analysis: Modelling and Control, 26(1), pp. 57-71. doi: 10.15388/namc.2021.26.20560.

Abstract

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.

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