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One dimensional Klein-Gordon (KG) equation is investigated in the domain ofconformable fractional calculus for one dimensional scalar potential namelygeneralized Hulthen potential. The conformable fractional calculus is based onconformable fractional derivative which is the most natural definition in noninteger order calculus. Fractional order differential equations can be solvedanalytically by means of this derivative operator. We obtained exact eigenvalueand eigenfunction solutions of local fractional KG equation and investigatedthe evolution of relativistic effects in correspondence with the fractionalorder.

Analytical solution of local fractional Klein-Gordon equation for the generalized Hulthen potential