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The main purpose of this article is to reconsider the theory of variational iteration method and embed it with Laplace transform to construct the conjoined technique variational iteration Laplace transform method. And then, by using the proposed method we solve a class of integral equations, especially fractional order Volterra type integro‐partial‐differential equations occurring in different fields of natural and social sciences. For this, we first turn to some prelude concepts and different types of equations especially integral equations of different kinds from the literature. Then, we will present step by step the embedded technique. Next, some fractional order model integral equations will be tackled using the proposed method along with some existing techniques, like the Adomian decomposition method and successive approximations method. The efficacy and authentication of the proposed technique will be analysed with the help of the obtained results and graphical exhibitions of the particular solved examples. Finally, use of the initiated method in the future for different types of equations occurring in different fields of science will be presented. [ABSTRACT FROM AUTHOR]