INVESTIGATION OF INTEGRAL BOUNDARY VALUE PROBLEM WITH IMPULSIVE BEHAVIOR INVOLVING NON-SINGULAR DERIVATIVE

Kamal Shah, Thabet Abdeljawad, Arshad Ali () and Manar A. Alqudah ()
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Kamal Shah: Department of Mathematics and Sciences, Prince Sultan University, P. O. Box 66833, 11586 Riyadh, Saudi Arabia2Department of Mathematics, University of Malakand, Chakdara Dir(L), 18000 Khyber Pakhtunkhwa, Pakistan
Thabet Abdeljawad: Department of Mathematics and Sciences, Prince Sultan University, P. O. Box 66833, 11586 Riyadh, Saudi Arabia3Department of Medical Research, China Medical University, Taichung 40402, Taiwan
Arshad Ali: Department of Mathematics, University of Malakand, Chakdara Dir(L), 18000 Khyber Pakhtunkhwa, Pakistan
Manar A. Alqudah: Department of Mathematical Sciences, Faculty of Sciences, Princess Nourah bint, Abdurahman University, P. O. Box 84428, Riyadh 11671, Saudi Arabia

FRACTALS (fractals), 2022, vol. 30, issue 08, 1-15

Abstract: This paper is devoted to investigating a class of impulsive fractional order differential equations (FODEs) with integral boundary condition. For the proposed paper, we use non-singular type derivative of fractional order which has been introduced by Atangana, Baleanu and Caputo (ABC). The aforesaid type problems have numerous applications in fluid mechanics and hydrodynamics to model various problems of flow phenomenons. We establish some sufficient conditions for the existence and uniqueness of solution to the proposed problem by using classical fixed point results due to Banach and Krasnoselskii. Further, on using tools of the nonlinear analysis, sufficient conditions are developed for Hyers–Ulam (HU) type stability results. A pertinent example is given to justify our results.

Keywords: Impulsive Problem; ABC Type Derivative; Integral Boundary Condition; Classical Fixed Point Results; HU Type Stability (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22402046

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