A computational approach for a system of coupled distributed-order fractional Klein–Gordon–Schrödinger equations

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In this study, a system of coupled distributed-order fractional Klein–Gordon–Schrödinger equations is introduced. The distributed-order fractional derivative is generated based on the Caputo fractional differentiation. The discrete Chebyshev polynomials are handled to construct computational approach for this system. To do this, fractional derivatives matrices (distribute-order and classical) of the expressed discrete polynomials are obtained. The intended approach is based on approximating the imaginary and real parts of the system solution by the mentioned polynomials and applying the extracted operational matrices, along with employing the collocation technique. The constructed scheme transforms the solution of the original system into solving a related algebraic system. Three test problems are examined to confirm the adequacy of the expressed collocation procedure.