Some qualitative analyses of neutral functional delay differential equation with generalized Caputo operator. (English) Zbl 1476.34159

Summary: In this paper, a new class of a neutral functional delay differential equation involving the generalized \(\psi\)-Caputo derivative is investigated on a partially ordered Banach space. The existence and uniqueness results to the given boundary value problem are established with the help of the Dhage’s technique and Banach contraction principle. Also, we prove other existence criteria by means of the topological degree method. Finally, Ulam-Hyers type stability and its generalized version are studied. Two illustrative examples are presented to demonstrate the validity of our obtained results.


34K37 Functional-differential equations with fractional derivatives
34K40 Neutral functional-differential equations
34K30 Functional-differential equations in abstract spaces
34K10 Boundary value problems for functional-differential equations
47N20 Applications of operator theory to differential and integral equations
34K27 Perturbations of functional-differential equations
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