Positive solutions for a class of two-term fractional differential equations with multipoint boundary value conditions

Abstract

In this article, we study the existence of positive solutions to a class of two-term fractional nonlocal boundary value problems. The existence and multiplicity of positive solutions are established by means of fixed point index theory. The nonlinearity f (t, x) permits a singularity at t = 0, 1 and x = 0.

On a fractional Caputo–Hadamard inclusion problem with sum boundary value conditions by using approximate endpoint property

“…In this direction, some researchers considered new applied modelings in recent years, which performed their proof techniques by combining the analytical and numerical methods such spline collocation method, [1][2][3][4] multiple positive solutions, [5][6][7][8][9][10][11][12][13][14][15] different computational studies, [16][17][18][19][20] and abstract views. [21][22][23][24][25][26][27][28][29][30] Later, alongside such problems, fractional differential inclusions as generalizations of the fractional differential equations attract the attention of many researchers. The theory of fractional differential inclusions contains a vast level of applied problems such as control theory, mechanics, economics modelings, and electrical engineering.…”

“…As you know, an importance and efficiency of this branch of mathematics has been caused to recent developments of fractional modelings and fractional boundary value problems. In this direction, some researchers considered new applied modelings in recent years, which performed their proof techniques by combining the analytical and numerical methods such spline collocation method, 1‐4 multiple positive solutions, 5‐15 different computational studies, 16‐20 and abstract views 21‐30 . Later, alongside such problems, fractional differential inclusions as generalizations of the fractional differential equations attract the attention of many researchers.…”

Positive Solutions for a Weakly Singular Hadamard-Type Fractional Differential Equation with Changing-Sign Nonlinearity

“…where α > β > 0, ω, τ are constants and D t α , D t β are Riemann-Liouville fractional derivatives. In practice, the study of the qualitative properties of solutions for the corresponding fractional models such as existence, uniqueness, multiplicity, and stability is necessary to analyze and control the model under consideration [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]. In [3], Zhang xðsÞdAðsÞ is denoted by a Riemann-Stieltjes integral and 0 < β ≤ 1 < α ≤ 2, α − β > 1, A is a function of bounded variation and dA can be a signed measure; the nonlinearity f ðt, x, yÞ may be singular at both t = 0, 1 and x = y = 0.…”

Existence and Nonexistence of Positive Solutions for High-Order Fractional Differential Equation Boundary Value Problems at Resonance

“…Fractional-order models can describe many processes more accurately than integer-order models, and a great deal of papers focusing on FBVPs appeared in recent years (see [14][15][16][17][18][19][20][21][22][23]). e nonlocal FBVPs have especially drawn much attention (see [24][25][26][27][28][29][30][31]). For instance, in [14], the authors investigated the Dirichlet-type FBVP:…”