Stability analysis of higher order nonlinear differential equations in β–normed spaces
Corresponding Author
Akbar Zada
Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan
Correspondence
Akbar Zada, Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan.
Email: [email protected]
Communicated by: S. Georgiev
Search for more papers by this authorShaleena Shaleena
Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan
Search for more papers by this authorTongxing Li
LinDa Institute of Shandong Provincial Key Laboratory of Network Based Intelligent Computing, Linyi University, Linyi, Shandong 276005, PR China
School of Information Science and Engineering, Linyi University, Linyi, Shandong 276005, PR China
Search for more papers by this authorCorresponding Author
Akbar Zada
Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan
Correspondence
Akbar Zada, Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan.
Email: [email protected]
Communicated by: S. Georgiev
Search for more papers by this authorShaleena Shaleena
Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan
Search for more papers by this authorTongxing Li
LinDa Institute of Shandong Provincial Key Laboratory of Network Based Intelligent Computing, Linyi University, Linyi, Shandong 276005, PR China
School of Information Science and Engineering, Linyi University, Linyi, Shandong 276005, PR China
Search for more papers by this authorAbstract
In this paper, we interrogate different Ulam type stabilities, ie, β–Ulam–Hyers stability, generalized β–Ulam–Hyers stability, β–Ulam–Hyers–Rassias stability, and generalized β–Ulam–Hyers–Rassias stability, for nth order nonlinear differential equations with integrable impulses of fractional type. The existence and uniqueness of solutions are investigated by using the Banach contraction principle. In the end, we give an example to support our main result.
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