| Summary: | In this research study, we establish some necessary conditions to check the uniqueness-existence of solutions for a general multi-term <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ψ</mi></semantics></math></inline-formula>-fractional differential equation via generalized <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ψ</mi></semantics></math></inline-formula>-integral boundary conditions with respect to the generalized asymmetric operators. To arrive at such purpose, we utilize a procedure based on the fixed-point theory. We follow our study by suggesting two numerical algorithms called the Dafterdar-Gejji and Jafari method (DGJIM) and the Adomian decomposition method (ADM) techniques in which a series of approximate solutions converge to the exact ones of the given <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ψ</mi></semantics></math></inline-formula>-RLFBVP and the equivalent <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ψ</mi></semantics></math></inline-formula>-integral equation. To emphasize for the compatibility and the effectiveness of these numerical algorithms, we end this investigation by providing some examples showing the behavior of the exact solution of the existing <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ψ</mi></semantics></math></inline-formula>-RLFBVP compared with the approximate ones caused by DGJIM and ADM techniques graphically.
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