Existence and uniqueness of classical and mild solutions of fractional Cauchy problem with impulses

Vishant Shah; Jaita  Sharma; Raju  K. George

doi:10.26637/mjm1101/005

Abstract

In this manuscript, we have established conditions for the existence and uniqueness of mild and classical solutions to the fractional order Cauchy problem by including and without including impulses over the completed norm linear space (Banach space). Conditions are established using the concept of generators and the generalised Banach fixed point theorem, which are weaker conditions than the previously derived conditions. We have also established the conditions under which a mild solution to the problem gives rise to a classical solution to the given problem. Finally, illustrations of the existence and uniqueness of the solution are provided to validate our derived results.

Keywords:

Existence of solution, Fractional evolution equation, Fixed point theorem, Impulsive conditions

Mathematics Subject Classification:

47D06, 34A12, 34A08, 35A01, 31C25

Authors Imprint References Funding Related Articles Downloads

Vishant Shah Faculty of Techonology \& Engineering, Department of Applied Mathematics, The Maharaja Sayajirao University of Baroda, Vadodara, Gujarat, India.
Jaita Sharma Faculty of Techonology \& Engineering, Department of Applied Mathematics, The Maharaja Sayajirao University of Baroda, Vadodara, Gujarat, India.
Raju K. George Department of Mathematics, Indian Institute of Space Science and Technology, Thiruvananthapuram, Kerala, India.

Pages: 66-79
Date Published: 01-01-2023
Vol. 11 No. 01 (2023): Malaya Journal of Matematik (MJM)

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