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The model case is driven by the following nonlocal double phase operator, $$ \\int \\!\\frac{|u(x)-u(y)|^{p-2}(u(x)-u(y))}{|x-y|^{n+sp}}\\, {\\rm d}y + \\int \\!a(x,y)\\frac{|u(x)-u(y)|^{q-2}(u(x)-u(y))}{|x-y|^{n+tq}}\\, {\\rm d}y, $$ where $q\\geq p$ and $a(\\cdot,\\cdot)\\geqq 0$. 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The model case is driven by the following nonlocal double phase operator, $$ \\int \\!\\frac{|u(x)-u(y)|^{p-2}(u(x)-u(y))}{|x-y|^{n+sp}}\\, {\\rm d}y + \\int \\!a(x,y)\\frac{|u(x)-u(y)|^{q-2}(u(x)-u(y))}{|x-y|^{n+tq}}\\, {\\rm d}y, $$ where $q\\geq p$ and $a(\\cdot,\\cdot)\\geqq 0$. 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