Abstract
In this paper, a new class of a neutral functional delay differential equation involving the generalized ψ -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.
Highlights
Fractional calculus has demonstrated high visibility and capability in the applications of various topics linked to physics, signal processing, mechanics, electromagnetics, economics, biology, and many more [1,2,3]
We considered and studied a fractional neutral functional delay differential equation involving a ψ-Caputo fractional derivative on a partially ordered Banach space
We proved the existence results with the help of the Dhage approximation technique, and by topological degree method for condensing maps
Summary
Fractional calculus has demonstrated high visibility and capability in the applications of various topics linked to physics, signal processing, mechanics, electromagnetics, economics, biology, and many more [1,2,3]. The iteration method due to Dhage has recently became an important tool for investigating the solution’s existence and approximate results of nonlinear hybrid FDEqs that have various scientific applications such as air motion, electricity, fluid dynamics, process control with nonlinear structures, and electromagnetism. This method can be extended to other functional differential equations (FuDEqs) classes. Motivated by the novel developments in ψ-fractional calculus, the solution’s existence, uniqueness, and UH stability of the proposed neutral functional differential equation (NFuDEq) is investigated in this research work. Some illustrative examples for supposed problem are provided at the end to validate our theoretical results
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