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In this article, we study a system of Hilfer (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>k</mi><mo>,</mo><mi>ψ</mi></mrow></semantics></math></inline-formula>)-fractional differential equations, subject to nonlocal boundary conditions involving Hilfer (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>k</mi><mo>,</mo><mi>ψ</mi></mrow></semantics></math></inline-formula>)-derivatives and (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>k</mi><mo>,</mo><mi>ψ</mi></mrow></semantics></math></inline-formula>)-integrals. The results for the mentioned system are established by using Mönch’s fixed point theorem, then the Ulam–Hyers technique is used to verify the stability of the solution for the proposed system. In general, symmetry and fractional differential equations are related to each other. When a generalized Hilfer fractional derivative is modified, asymmetric results are obtained. This study concludes with an applied example illustrating the existence results obtained by Mönch’s theorem.