On a generalized fractional nonlinear differential equation

Abstract In this work, we consider one of the most generalized variant of fractional nonlinear differential equations involving <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mrow> <m:mi mathvariant="monospace">k</m:mi> <m:mo>,</m:mo> <m:mi>ψ</m:mi> </m:mrow> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:math> $(\mathtt{k},\psi )$ -Hilfer fractional derivative under multiple boundary conditions. Using the topological degree theory and a fixed point theorem, we prove a new existence and uniqueness results. Then, we investigate the Ulam–Hyers stability of the solutions. Our result recovers the majority of the previous existing results. To validate the relevance of our finding, an illustrative example is presented.