Abstract
In this paper, we derive some sufficient conditions which ensure the existence and uniqueness of a solution for a class of nonlinear three point boundary value problems of fractional order implicit differential equations (FOIDEs) with some boundary and impulsive conditions. Also we investigate various types of Hyers–Ulam stability (HUS) for our concerned problem. Using classical fixed point theory and nonlinear functional analysis, we obtain the required conditions. In the last section we give an example to show the applicability of our obtained results.
Highlights
1 Introduction Differential equations of fractional order have been attracted the attention of researchers in the last few decades
We model and describe such type of evolutionary processes via differential equations with some impulsive conditions
There are many evolutionary processes related to pharmacotherapy, hemodynamics equilibrium of a person, introduction of bloodstream in the body and problems related to economical and national income, which cannot be accurately described by classical implicit impulsive differential equations
Summary
Differential equations of fractional order have been attracted the attention of researchers in the last few decades. There are many evolutionary processes related to pharmacotherapy, hemodynamics equilibrium of a person, introduction of bloodstream in the body and problems related to economical and national income, which cannot be accurately described by classical implicit impulsive differential equations. In such a situation the fractional order implicit impulsive differential equations are proved as powerful tools. Ali et al Advances in Difference Equations [17], exponential stability [18] and Hyers–Ulam stability, have been introduced Among all these concepts, Hyers–Ulam type stability analysis has been considered a relatively easy and simple way of studying the stability of solutions to fractional order implicit differential equations (FOIDEs).
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