<p>In this paper, we study fuzzy Volterra integro-dynamic equations with fuzzy kernels under <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\Delta _{\psi }\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="normal">Δ</mi> <mi>ψ</mi> </msub> </math></EquationSource> </InlineEquation>-differentiability for <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\mathcal {S}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">S</mi> </math></EquationSource> </InlineEquation>-linearly correlated fuzzy processes on time scales. In particular, we propose a fuzzy Adomian decomposition method to solve these equations, demonstrating that it leads to a series that approaches the unique solution of the fuzzy Volterra integro-dynamic equations. Additionally, we investigate the relationships between fuzzy initial value problems for nth-order fuzzy dynamic equations and fuzzy Volterra integral equations, as well as, between fuzzy Volterra integro-dynamic equations and fuzzy initial value problems for <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\mathcal {S}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">S</mi> </math></EquationSource> </InlineEquation>-linearly correlated fuzzy processes on time scales. As a consequence of the developed theory, the fuzzy Adomian decomposition method is applied to solve initial value problems for <i>n</i>th order fuzzy dynamic equations. To demonstrate its effectiveness, an application to fuzzy damped spring-mass systems is presented. Several illustrative examples are provided to demonstrate our results, as well.</p>