Initial Value Problem for Stochastic Hyprid Hadamard Fractional Differential Equation

Abstract

In this paper, we discuss the existence of solutions for a stochastic initial value problem of Hyprid fractional dierential equations of Hadamard type given by 
 
 where HD is the Hadamard fractional derivative, and is the Hadamard fractional integral and be such that are investigated. The fractional calculus and stochastic analysis techniques are used to obtain the required results.

Analytical analysis of fractional-order sequential hybrid system with numerical application

“…In addition, hybrid differential equations can be found in several subjects of mathematics and physics, such as the deflection of a curved beam with constant or varying cross-section, a three-layer beam, electromagnetic waves, or gravity-driven flows, and so on. For details, we refer the readers to [15][16][17][18][19][20][21][22][23][24][25].…”

On the Hybrid Fractional Differential Equations with Fractional Proportional Derivatives of a Function with Respect to a Certain Function

“…Recently, a new class of mathematical modelings based on hybrid fractional differential equations with hybrid or non-hybrid boundary value conditions have accomplished a large inquisitiveness of many researchers using different techniques (see, for example, [22][23][24][25]). Fractional hybrid differential equations can be employed in modeling and describing non-homogeneous physical phenomena that take place in their form.…”

Existence Results for Hybrid Stochastic Differential Equations Involving $\psi$-Hilfer Fractional Derivative

“…In [24], Vivek et al investigated dynamics and stability of pantograph equations via Hilfer fractional derivative. Moreover, stochastic perturbation is unavoidable in nature and hence it is important and necessary to consider stochastic effect into the investigation of FDEs, see [5,6,8,11].…”