Existence and Ulam stability for impulsive generalized Hilfer-type fractional differential equations

Abstract

Abstract In this manuscript, we examine the existence and the Ulam stability of solutions for a class of boundary value problems for nonlinear implicit fractional differential equations with instantaneous impulses in Banach spaces. The results are based on fixed point theorems of Darbo and Mönch associated with the technique of measure of noncompactness. We provide some examples to indicate the applicability of our results.

Keywords

• Boundary value problem
• Generalized Hilfer fractional derivative
• Fractional integral
• Impulses
• Fixed point
• Measure of noncompactness