Kishor D. Kucche

On existence results and qualitative properties of mild solution of semilinear mixed Volterra-Fredholm functional integrodifferential equations in Banach spaces

In this paper, we prove the existence results, uniqueness, continuous dependence on initial functions and on parameters of mild solution of semilinear mixed Volterra-Fredholm functional integrodifferential equations in Banach spaces. The closeness and continuous dependence of the mild solution on the right-hand side of the equation is also established. Our analysis is based on the theory of strongly continuous semigroup, the nonlinear alternative of Leray-Schauder and the integral inequality established by Pachpatte. An example is given to illustrate the results.

Stability via successive approximation for nonlinear implicit fractional differential equations

Abstract In this paper we are concerned with nonlinear implicit fractional differential equations with initial conditions. We prove the existence and uniqueness results by using modified version of contraction principle. Further, our prime aim is to present various Ulam-Hyers stability and Eα-Ulam-Hyers stability results via successive approximation method.

CONTROLLABILITY OF NON-DENSELY DEFINED ABSTRACT MIXED VOLTERRA–FREDHOLM NEUTRAL FUNCTIONAL INTEGRODIFFERENTIAL EQUATIONS

In this paper we establish the controllability result for class of mixed Volterra–Fredholm neutral functional integrodifferential equations in Banach spaces where the linear part is non-densely defined and satisfies the resolvent estimate of the Hille–Yosida condition. The results are obtained using the integrated semigroup theory and the Sadovskiis fixed point theorem.

Stability of ψ-Hilfer impulsive fractional differential equations

Abstract In this paper, we investigate the sufficient conditions for existence and uniqueness of solutions and δ -Ulam–Hyers–Rassias stability of an impulsive fractional differential equation involving ψ -Hilfer fractional derivative. Fixed point approach is used to obtain our main results. Finally, we present examples to illustrate the results.

Ulam–Hyers Stability of Integrodifferential Equations in Banach Spaces via Pachpatte’s Inequality

In this paper, Pachpatte’s inequality is employed to discuss the Ulam–Hyers stabilities for Volterra integrodifferential equations and Volterra delay integrodifferential equations in Banach spaces on both finite and infinite intervals. Examples are given to show the applicability of our obtained results.