Abstract
We present some results on the existence, uniqueness and Hyers–Ulam stability to the solution of an implicit coupled system of impulsive fractional differential equations having Hadamard type fractional derivative. Using a fixed point theorem of Kransnoselskii’s type, the existence and uniqueness results are obtained. Along these lines, different kinds of Hyers–Ulam stability are discussed. An example is given to illustrate the main theorems.
Highlights
Fractional calculus is one of the emerging areas of investigation
fractional differential equations (FDEs) serve as an excellent tool for the description of hereditary properties of various materials and processes [3]
The impulsive FDEs are of great value
Summary
Fractional calculus is one of the emerging areas of investigation. The fractional differential operators are used to model several physical phenomena in a much better form than ordinary differential operators, which are local. The existence and uniqueness of the solution of sequential fractional differential equations with Hadamard derivative have been explored by Klimek [55]. Wang et al [56] discussed the existence, blowing-up solutions and Ulam–Hyers stability of fractional differential equations with Hadamard derivative by using some classical methods.
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