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In this study, we concentrate on an important class of ordered hyperstructures with symmetrical hyperoperations, which are called ordered Krasner hyperrings, and discuss strong derivations and homo-derivations. Additionally, we apply our results on nonzero proper hyperideals to the study of derivations of prime ordered hyperrings. This work is a pioneer in studies on structures such as hyperideals and homomorphisms of an ordered hyperring with the help of derivation notation. Finally, we prove some results on 2-torsion-free prime ordered hyperrings by using derivations. We show that if <i>d</i> is a derivation of 2-torsion-free prime hyperring <i>R</i> and the commutator set <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>[</mo><mi>l</mi><mo>,</mo><mi>d</mi><mo>(</mo><mi>q</mi><mo>)</mo><mo>]</mo></mrow></semantics></math></inline-formula> is equal to zero for all <i>q</i> in <i>R</i>, then <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>l</mi><mo>∈</mo><mi>Z</mi><mo>(</mo><mi>R</mi><mo>)</mo></mrow></semantics></math></inline-formula>. Moreover, we prove that if the commutator set <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>d</mi><mo>(</mo><mi>l</mi><mo>)</mo><mo>,</mo><mi>q</mi><mo>)</mo></mrow></semantics></math></inline-formula> is equal to zero for all <i>l</i> in <i>R</i>, then <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>d</mi><mo>(</mo><mi>R</mi><mo>)</mo><mo>,</mo><mi>q</mi><mo>)</mo><mo>=</mo><mn>0</mn></mrow></semantics></math></inline-formula>.