Application of Laplace transform to solve fractional integro-differential equations

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This paper reveals the solutions to several families of fractional integro-differential equations through the application of a simple fractional calculus method. This approach results in various interesting consequences and also extends the classical Frobenius method. The provided approach is primarily based on established theorems concerning particular solutions of fractional integro-differential equations using the Laplace transform and the extension coefficients of binomial series. Additionally, an illustrative example of such fractional integro-differential equations is presented.