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The existence and numerical solution for a \(k\)-dimensional system of multi-term fractional integro-differential equations. (English) Zbl 1434.45005

The paper is concerned with existence, uniqueness and numerical solution of \(k\)-dimensional systems of multi-term fractional differential equations viewed as a boundary value problem. The paper is fairly classical in its approach: existence and uniqueness theory is presented and then numerical schemes based on shifted Chebyshev and shifted Legendre polynomials are developed and analysed. The authors conclude with some numerical examples, taking account of solutions with varying levels of smoothness.

MSC:

45J05 Integro-ordinary differential equations
65R20 Numerical methods for integral equations
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