Abstract
In this manuscript, we investigate a sort of fractional neutral integro-differential equations with impulsive outcomes and extend the formula of general solutions for the impulsive fractional neutral integro-differential system in a Banach space. By using the analysis of the limit case and the operator generating compact semigroup, we derive the main results. Finally, an example is discussed to illustrate the efficiency of the results.
Highlights
Fractional calculus is a field of mathematics study that grows out of traditional definitions of calculus integral and derivative operators in much the same way fractional exponents are an outgrowth of exponents with integer value
Liu et al [17] established the approximate controllability of impulsive fractional neutral evolution equations with RL fractional derivatives by using the Banach contraction principle
5 Conclusion In this manuscript, we have studied the local existence for an impulsive fractional neutral integro-differential system with Riemann–Liouville fractional derivatives in a Banach space
Summary
Fractional calculus is a field of mathematics study that grows out of traditional definitions of calculus integral and derivative operators in much the same way fractional exponents are an outgrowth of exponents with integer value. The following fractional order integro-differential equation in a Banach space using the Caputo fractional derivative: M, t ≥ 0, t = tk, was mentioned by Gou and Li [8], and they established the local and global existence of mild solution to an impulsive fractional semilinear integro-differential equation with noncompact semigroup.
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