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  Abstract.   The Sturm-Liouville boundary value problem of the multi-order fractional differential equation  is studied. Results on the existence of solutions are established. The analysis relies on a weighted function space and a fixed point theorem. An example is given to illustrate the efficiency of the main theorems.

کلیدواژه ها:

solution ، multi-order fractional differential equation ، Sturm-Liouville boundary value problems ، fixed-point theorem