On a class of differential inclusions in the frame of generalized Hilfer fractional derivative

Abstract

<abstract><p>In the present paper, we extend and develop a qualitative analysis for a class of nonlinear fractional inclusion problems subjected to nonlocal integral boundary conditions (nonlocal IBC) under the $ \varphi $-Hilfer operator. Both claims of convex valued and nonconvex valued right-hand sides are investigated. The obtained existence results of the proposed problem are new in the frame of a $ \varphi $-Hilfer fractional derivative with nonlocal IBC, which are derived via the fixed point theorems (FPT's) for set-valued analysis. Eventually, we give some illustrative examples for the acquired results.</p></abstract>

Study of (k,Θ)-Hilfer fractional differential and inclusion systems on the glucose graph

“…In 2000, Hilfer proposed the generalized Riemann-Liouville fractional derivative for short Hilfer fractional derivative [14] , including Riemann-Liouville fractional derivative and Caputo fractional derivative. Subsequently, fractional differential equations with Hilfer fractional derivatives have been studied by many authors and are widely used in physics [15] , [16] , [17] , [18] , [19] , [20] , [21] , [22] . For example, in 2023, Sivasankar and Udhayakumar [20] studied a new set of sufficient conditions for the existence of mild solutions for Hilfer fractional neutral stochastic evolution equations via almost sectorial operators with delay.…”

New refinements of the Hermite–Hadamard inequalities based on ψ-Hilfer fractional integrals

“…Fractional integrals solved many integrals in mathematics. Fractional integral types, which are also used in the field of inequality, have provided new extensions, refinements, and, generalizations in this field [4,10,14,17,18,21]. Insome studies, by using the convexity of the function, in some research, by making use of the bounds of the second derivative, many studies that will contribute to the literature have been made.…”