Existence of the Class of Nonlinear Hybrid Fractional Langevin Quantum Differential Equation with Dirichlet Boundary Conditions

Abstract

In this paper, we investigate the existence results for nonlinear fractional q-difference equations with two different fractional orders supplemented with the Dirichlet boundary conditions. Our main existence results are obtained by applying the contraction mapping principle and Krasnoselskii’s fixed point theorem. An illustrative example is also discussed.

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

“…As a basic mathematical model, fractional differential equations are often used in many practical applications [5] , [6] , [7] , [8] , [9] , [10] . For qualitative analysis of solutions of fractional differential equations, see [11] , [12] , [13] .…”

Existence and stability results for non-hybrid single-valued and fully hybrid multi-valued problems with multipoint-multistrip conditions

“…Fractional hybrid differential inclusions (FHDIs) and fractional hybrid differential equations (FHDEs) of the first and second types are the generalizations of standard FDIs and FDEs which were introduced by Dhage et al [17] in 2010 and also by Zhao et al [18] in 2011. Immediately, these hybrid FBVPs found their place in various computations and mathematical modelings so that we highlight some of the strong works in this regard by naming the papers from Baleanu et al [19], Nagajothi et al [20], Matar et al [21], Khan et al [22], Mohammadi et al [23], etc. Along with these, an extended type of boundary conditions (BCs) entitled multi-point and multi-strip conditions were introduced in some models.…”