Some Results on Fractional Boundary Value Problem for Caputo-Hadamard Fractional Impulsive Integro Differential Equations

Abstract

The results for a new modeling integral boundary value problem (IBVP) using Caputo-Hadamard impulsive fractional integro-differential equations (C-HIFI-DE) with Banach space are investigated, along with the existence and uniqueness of solutions. The Krasnoselskii fixed-point theorem (KFPT) and the Banach contraction principle (BCP) serve as the basis of this unique strategy, and are used to achieve the desired results. We develop the illustrated examples at the end of the paper to support the validity of the theoretical statements.

On Some Impulsive Fractional Integro-Differential Equation with Anti-Periodic Conditions

“…The HFD, in contrast to the Caputo and Riemann-Liouville derivatives, has an arbitrary-order logarithmic function (log α − log β) rather than (α − β). The expression of the HFD can be understood as a generalization operator (refer, for example, to [4][5][6][7][8][9][10][11]). This is only one more crucial aspect of the HFD.…”