This article deals with a nonlinear implicit fractional differential equation nonlocal integral-multipoint boundary conditions in the frame of Hilfer derivative. The existence and uniqueness results are obtained by using fixed point theorems Krasnoselskii Banach. Further, to demonstrate effectiveness main results, suitable examples granted.

In this paper, two significant inequalities for the Hilfer fractional derivative of a function in space ACγ([0,b],Rn), 0≤γ≤1 are obtained. We first verified extremum principle derivative. addition, we estimated at its extreme points. Furthermore, derived and proved maximum nonlinear differential equation. Finally, analyzed solutions Our results generalize extend some obtained theorems on topic.

in this paper, we prove the existence and uniqueness results to the random fractional functional differential equations under assumptions more general than the lipschitz type condition. moreover, the distance between exact solution and appropriate solution, and the existence extremal solution of the problem is also considered.

Using the Schauder fixed point theorem, we prove existence of impulsive fractional differential equations using Hilfer derivative and nearly sectorial operators in this paper. We’ve gone over two scenarios where related semigroup is compact noncompact for purpose. We also go an example to back up main points.

In this paper, we investigate infinite interval problems for the fractional evolution equations with Hilfer derivative. By using generalized Ascoli–Arzelà theorem and some new techniques, prove existence of mild solutions when semigroup is compact as well noncompact. addition, an example provided to illustrate results.

the present study aims at indicating the existence and uniqueness result of system in extended colombeaualgebra. the caputo fractional derivative is used for solving the system of odes. in addition, rieszfractional derivative of colombeau generalized algebra is considered. the purpose of introducing rieszfractional derivative is regularizing it in colombeau sense. we also give a solution to a n...