<p>This paper investigates the results concerning the approximate numerical solutions of the non-integer differential equations with multiple delays. The multiple delays may not lie on the same mesh, so in this paper the aim is to deal with such delays using a uniform mesh. The derivative taken in the differential equation is the Caputo fractional derivative of arbitrary order. Our methodology is a combination of the Haar wavelet collocation method (HWCM) and the Lagrange interpolation. In the HWCM, the derivative inside the integral of the fractional derivative is taken to be in the form of an infinite series of the Haar functions, and then a numerical approximation of the infinite sum is taken. The Lagrange interpolating polynomial is used to make approximations of the delays so that we can work with the mesh given by the HWCM. The proposed scheme is found to be convergent and its numerical efficiency is demonstrated with the help of several examples. The error in <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L_2\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>L</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation> norm and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(L_\infty \)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>L</mi> <mi>∞</mi> </msub> </math></EquationSource> </InlineEquation> norm are used to show the numerical accuracy of the methods. The numerical simulations are compared with existing results in the literature.</p>