Symmetry group classification for one-dimensional elastodynamics problems in nonlocal elasticity

The symmetry groups of one-dimensional elastodynamics problem of nonlocal elasticity are investigated and we get a classification for the problem. The determining equations of the system of Fredholm integro-differential equations corresponding to one-dimensional nonlocal elasticity equation are found and solved. We get the differential equations that include the kernel function and the independent term. The symmetry groups are determined using these functions. We compare the results of one-dimensional nonlocal elasticity with the results of the Voltera integro-differential equation corresponding to one-dimensional visco-elasticity equation in the conclusion section of the manuscript.