“…The traditional Riemann-Liouville(RL) and Caputo fractional derivatives are obtained in special circumstances for λ = 0, and this new fractional operator depends on the parameter λ. Due to its use in physics, groundwater hydrology, poroelasticity, geophysical flow, finance [7,11,12,21,22,32], the tempered fractional derivative has recently gained popularity as a subject of study. In [40], Zaky studied the well-posedness of the solution to the following two-point nonlinear tempered fractional boundary value problem(TFBVP) e 0 D α,λ r ϖ(r) = ψ(r, ϖ(r)) r ∈ [0, s], α ∈ (0, 1), αϖ(0) + ße λs ϖ(s) = γ.…”