Existence of Positive Solutions to a Boundary Value Problem for a Delayed Singular High Order Fractional Differential Equation With Sign-Changing Nonlinearity

Existence and multiplicity of solutions for boundary value problem of singular two-term fractional differential equation with delay and sign-changing nonlinearity

“…Recently, fractional differential equations have been extensively studied, among which the existence of positive solutions to fractional differential equations was considered in [1, 8, 10-12, 15, 16, 19, 20] and [6,22]. In particular, the nonlinear terms of the problems studied in [8,[10][11][12]19] can change sign and are singular at time or space variables. In practical problems, delay is a nonnegligible factor, which can reasonably express the influence of the past on the present.…”

“…In practical problems, delay is a nonnegligible factor, which can reasonably express the influence of the past on the present. Therefore the delay differential equation has a wide range of applications in control theory, signal processing, biology, finance, and many other fields [4,10,12,14,21]. In addition, unlike the above research problems, the fractional differential equations of two terms are studied in [2,3,17,18].…”

On the boundary value problems of piecewise differential equations with left-right fractional derivatives and delay

“…0 + y(t) + λI p 1 − I q 0 + h t, y(t) = f t, y(t) , t ∈ J := [0, 1], y(0) = y(ξ) = 0, y(1) = δy(µ), 0 < ξ < µ < 1, where 1 < α 2, 0 < β 1 and p, q > 0, f, h : [0, 1] × R → R are given continuous functions, and δ, λ, µ ∈ R are constants. At the same time, the differential equations with delay have many successful applications in the fields of communication engineering, population control and so on; see [1,9,20,21,26,28,35].…”

Extremal Solutions for a Class of Tempered Fractional Turbulent Flow Equations in a Porous Medium

“…Particularly, if the model is of fractional order, then it can describe turbulent flow in a porous medium [5][6][7][8][9][10]. On the contrary, fractional-order derivative has nonlocal characteristics; based on this property, the fractional differential equation can also interpret many abnormal phenomena that occur in applied science and engineering, such as viscoelastic dynamical phenomena [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29], advection-dispersion process in anomalous diffusion [30][31][32][33][34], and bioprocesses with genetic attribute [35,36]. As a powerful tool of modeling the above phenomena, in recent years, the fractional calculus theory has been perfected gradually by many researchers, and various different types of fractional derivatives were studied, such as Riemann-Liouville derivatives [16,, Hadamardtype derivatives [63][64][65][66][67][68][69][70][71], Katugampola-Caputo derivatives [72], conformable derivatives…”