A uniqueness method to a new Hadamard fractional differential system with four-point boundary conditions

Abstract

In this article, we discuss a new Hadamard fractional differential system with four-point boundary conditions where are two parameters with , are two real numbers and , , are constants, and are the Hadamard fractional derivatives of fractional order. Based upon a fixed point theorem of increasing φ--concave operators, we establish the existence and uniqueness of solutions for the problem dependent on two constants .

The Extremal Solution To Conformable Fractional Differential Equations Involving Integral Boundary Condition

“…Fractional calculus is an excellent tool for the description of the process of mathematical analysis in various areas of finance, physical systems, control systems and mechanics, and so forth [1][2][3][4][5]. Many methods are used to study various fractional differential equations, such as fixed point index theory [6], iterative method [7][8][9], theory of linear operator [10,11] sequential techniques, and regularization [12], fixed point theorems [13][14][15][16][17], the Mawhin continuation theorem for resonance [18][19][20][21][22], the variational method [23]. The definition of the fractional order derivative used in the aforementioned results is either the Caputo or the Riemann-Liouville fractional order derivative.…”

Existence and convergence results of meromorphic solutions to the equilibrium system with angular velocity

“…(t, n )( n -) dt = 0.To this end, by(13), there exists some positive constant d such that n τ ,λ < d and u τ ,λ < d, for n ∈ N, n → u strongly in L q (R) and a.e. in R.…”

“…As one of the universal equilibrium systems used in the description of pattern formation in spatially extended dissipative systems, the general equilibrium differential equation can also be found in the study of convective hydrodynamics, plasma confinement in toroidal devices, viscous film flow, and bifurcating solutions of the modified equilibrium differential equation [6,10,11]. In recent years, some references such as Sheng et al [12], Zhai et al [13], Zhang [14], Wu et al [15], Sun et al [16], Li et al [17], Bai and Sun [18], Wang et al [19], and so on, introduced many beautiful patterns to satisfy practical requirements of modern computing systems with multi-processors. There is the potential of considering the linearization characteristics to be further developed for the system of equilibrium boundary value problems.…”

Positive Solutions for a Hadamard Fractional p-Laplacian Three-Point Boundary Value Problem

“…Hadamard fractional-order problems were briefly discussed in the literature; see [53][54][55][56][57][58][59][60][61][62][63][64][65][66][67][68][69][70][71][72] and the references therein. Yang in [53] used the comparison principle and the monotone iterative technique combined with the subsolution and supersolution method to study the existence of extremal solutions for Hadamard fractional differential equations with Cauchy initial value conditions…”