Abstract
We present some new results on the approximation of solutions of a special type of fractional boundary-value problem. The focus of our research is a system of three fractional differential equations of the mixed order, subjected to the so-called “interpolation” type boundary restrictions. Under certain conditions, the aforementioned problem is simplified via a proper parametrization technique, and with the help of the numerical-analytic method, the approximate solutions are constructed.
Highlights
Differential equations of the fractional order have a wide spectrum of applications, since they are often used to model problems in fluid dynamics, finance, biology, physics, engineering, etc
During the last few years, a number of papers devoted to the numerical-analytic methods of approximation of solutions of the fractional ordinary and partial differential equations were published
Since the approach of the numerical-analytic method [32] was appied to the fractional differential systems for the first time in [25,26,27,28], it is resonable to give an overview of the results that will allow the reader to follow and will open up possible perspectives for future research in this direction
Summary
Differential equations of the fractional order have a wide spectrum of applications, since they are often used to model problems in fluid dynamics, finance, biology, physics, engineering, etc. During the last few years, a number of papers devoted to the numerical-analytic methods of approximation of solutions of the fractional ordinary and partial differential equations were published. To construct the approximate solutions of the studied problems, the numerical-analytic method, based on the successive iterations, was used This technique was originally suggested and successfully applied to the boundary-value problems for ordinary differential systems with strong nonlinearities in the equations, and in the boundary conditions (see [29,30,31,32]). As a result: these techniques might be further studied in the more complicated cases of boundary conditions (e.g., two- and multipoint nonlinear boundary constraints), widely appearing in the mathematical models of applied sciences
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