On implicit impulsive Langevin equation involving mixed order derivatives

Abstract

In this paper, we consider a nonlocal boundary value problem of nonlinear implicit impulsive Langevin equation involving mixed order derivatives. Sufficient conditions are constructed to discuss the qualitative properties like existence and Ulam's stability of the proposed problem. The main result is verified by an example.

Analysis ofq‐fractional implicit boundary value problems having Stieltjes integral conditions

“…Many researchers used different fixed point theorems and developed different results for the existence of solutions of boundary value problems. For details, we refer the reader to other works 21‐27 . On the other hand, the study of coupled systems of differential equations is also very significant because these types of systems appear naturally in many problems of applied nature.…”

“…For details, we refer the reader to other works. [21][22][23][24][25][26][27] On the other hand, the study of coupled systems of differential equations is also very significant because these types of systems appear naturally in many problems of applied nature. For detail and examples, the reader may see previous studies.…”

Analysis of boundary value problem with multi-point conditions involving Caputo-Hadamard fractional derivative

“…One of the main factors that represent the utility/prevalence of the subject is that fractional order derivatives and integrals are shown to be better devices for the representation of real components than integer orders. We refer the reader to the papers [6,8,11,18,19,20,21,22,23,26,27,4,30,3,17] for examples and information, and the references cited therein. A large part of the work on the subject was found to depend on Riemann-Liouville and Caputo FDEs.…”

Well‐posedness and Hyers‐Ulam results for a class of impulsive fractional evolution equations

“…Wang et al 25 are the first mathematician who investigated the Ulam‐type stability and data dependence for FDE. For the detailed study of Ulam‐type stability, we recommend other studies 13,14,24,26‐34 …”

“…For the detailed study of Ulam-type stability, we recommend other studies. 13,14,24,[26][27][28][29][30][31][32][33][34] Recently, Sutar and Kucche 35 studied the following impulsive FDE:…”