The existence and stability results of nonlocal integro-differential boundary value problemswith Hilfer derivative of order ω ∈ (1, 2) have been investigated. A new definition of thefractional derivative was introduced by R. Hilfer. He named it as the left-sided (right-sided)generalized Riemann-Liouville (R-L) derivative of order ω ∈ (0, 1) and a type τ ∈ [0, 1]. Manyauthors call it the Hilfer derivative. Such derivative interpolates between the R-L and Caputoderivative. The fixed point theorems of Banach and Schaefer are two commonly used fixedpoint theorems that are applied to our results. To demonstrate the effectiveness and applicabilityof our theoretical conclusions and two-step Lagrange polynomial interpolation were usedto solve three numerical results and their application is used in the last part.