<p>In this paper, we investigate the uniqueness problems of meromorphic functions with partially shared values. Under the condition that the hyper-order of the meromorphic function is strictly less than 1, we establish two uniqueness results for a non-constant meromorphic function <i>f</i> that partially shares four small functions with its shift <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(f(z+\eta )\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>f</mi> <mo stretchy="false">(</mo> <mi>z</mi> <mo>+</mo> <mi>η</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>. This leads to the conclusion <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(f(z)\equiv f(z+\eta )\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>f</mi> <mo stretchy="false">(</mo> <mi>z</mi> <mo stretchy="false">)</mo> <mo>≡</mo> <mi>f</mi> <mo stretchy="false">(</mo> <mi>z</mi> <mo>+</mo> <mi>η</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> through a novel approach. Our results generalize and expand upon several previous results in the field. Additionally, we provide examples that demonstrate the existence of meromorphic functions satisfying the conditions of our theorems.</p>