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In this article, we study the existence and uniqueness results for a separate nonlinear Caputo fractional sum-difference equation with fractional difference boundary conditions by using the Banach contraction principle and the Schauder&#8217;s fixed point theorem. Our problem contains two nonlinear functions involving fractional difference and fractional sum. Moreover, our problem contains different orders in <inline-formula> <math display="inline"> <semantics> <mrow> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </semantics> </math> </inline-formula> fractional differences and <inline-formula> <math display="inline"> <semantics> <mrow> <mi>m</mi> <mo>+</mo> <mn>1</mn> </mrow> </semantics> </math> </inline-formula> fractional sums. Finally, we present an illustrative example.