Existence and continuous dependence results for fractional evolution integrodifferential equations of order <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"> <mml:mrow> <mml:mi>r</mml:mi> <mml:mo>∈</mml:mo> <mml:mo stretchy="true">(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mn>2</mml:mn> <mml:mo stretchy="true">)</mml:mo> </mml:mrow> </mml:math>
Yong‐Ki Ma, Marimuthu Mohan Raja, V. Vijayakumar, Anurag Shukla, Wedad Albalawi, Kottakkaran Sooppy Nisar
Abstract
The article analyzes the existence of Caputo fractional evolution integrodifferential equations of order 1<r<2 in Hilbert space with delay. A new set of adequate requirements for the existence outcomes of fractional delay evolution integrodifferential equations have been developed and are shown using the fractional derivative, Krasnoselskii’s fixed point theorem, and Henry-Gronwall inequalities. In addition, for the provided system, we developed continuous dependence results. Afterward, we apply our findings to the concept of nonlocal conditions. Then, to demonstrate our primary outcomes, two examples are given.
Topics & Concepts
MathematicsHilbert spaceFractional calculusOrder (exchange)Set (abstract data type)Fixed-point theoremApplied mathematicsDerivative (finance)Space (punctuation)Pure mathematicsComputer scienceProgramming languageEconomicsFinanceFinancial economicsOperating systemNonlinear Differential Equations AnalysisFractional Differential Equations SolutionsDifferential Equations and Boundary Problems