Existence and stability analysis of nth order multi term fractional delay differential equation

• Published in: Chaos, solitons and fractals solitons and fractals, 2022-02, Vol.155, Article 111709
• Main Authors: ur Rahman, Ghaus, Agarwal, Ravi P., Ahmad, Dildar
• Format: Article
• Language: English
• Subjects: Existence & uniqueness of solution; Fractional differential equations; Functional stability; Multi term operators
• ISSN: 0960-0779; 1873-2887
• DOI: 10.1016/j.chaos.2021.111709

•To formulate a differential equation of fractional order with delay and multi term differential operators.•To explore results related to the existence and uniqueness of the solution of the model under consideration.•To demonstrate that solution of the fractional order multi term differential equation satisfy definition of four kinds of functional stability.•To provide examples for showing the authenticity of the obtained results. Study of fractional differential equations equipped with multi term operator have been carried out in the recent years. Several novel models need to be formulated. Therefore, keeping in view the importance of multi term differential operators in the study of differential equations, we propose a model of nth order multi term fractional delay differential equation (MTFDDE). We will provide results related to solution’s existence, and its uniqueness as well as will explore results related to four different kinds of functional stability. To get the results under consideration, standard fixed point theorems will be used. Moreover, functional stability results are obtained successfully and at last data dependence results are elaborated with the help of different results.