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.
Highlights
Fractional integration and differentiation are generalizations of integer-order calculus to noninteger ones
It is demonstrated in literature that fractional calculus can play a justifiable and beneficial role in the modeling of various phenomena e.g. science and engineering [2, 3, 6, 25, 29, 30, 35,36,37, 42]
This section is a discussion about the convergence of the generalization of squared remainder minimization (GSRM) method for the multipoint fractional differential equations of the form (1)
Summary
Fractional integration and differentiation are generalizations of integer-order calculus to noninteger ones. Another version of fractional-order derivative, which uses the generalized Mittag–Leffler function with strong memory as nonlocal and nonsingular kernel in [5]. The third section deals with a generalization of squared remainder minimization (GSRM) method for the multi-point fractional differential equations.
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