A study on the existence of solutions of generalized fractional differential equations

Abstract

Fractional calculus is a branch of Mathematics that studies the derivatives and integrals of non-integer orders. Studying generalized fractional differential equations is significant as it allows broader exploration of mathematical models, incorporating various kernels in the y- Caputo and y- Hilfer fractional differential equations. This versatility leads to the formulation of diverse fractional differential equations involving classical operators, offering a more comprehensive understanding of complex phenomena in diverse fields. We investigated the existence and uniqueness of neutral fractional differential equation, Impulsive fractional neutral functional differential equation and k system offractional neutral differential equation involving -Caputo fractional operator, the existence of Hybrid fractional differential equations with both initial and boundary conditions involving -Hilfer fractional derivative. Also investigated the existence, uniqueness, Ulam Hyers, generalized Ulam Hyers, Ulam Hyers Rassias and generalized Ulam Hyers stabilities for y -Caputo neutral functional differential equation and y Hilfer fractional neutral functional differential equations. Examples illustrating the results and graphs are given.