Abstract
In this article, we are pleased to investigate multiple positive solutions for a system of Hadamard fractional differential equations with (p_{1}, p_{2}, p_{3})-Laplacian operator. The main results rely on the standard tools of different fixed point theorems. Finally, we demonstrate the application of the obtained results with the aid of examples.
Highlights
The majority of the aforesaid analysis on the topic is based upon fractional differential equations and Hadamard fractional derivatives involving many numerous applications in a variety of fields such as control theory, electrical circuits, biology, physics, and finance [1,2,3,4,5,6,7,8,9,10]
The results of multiplicity of positive solutions for a system of fractional differential equations which are subject to various levels of boundary conditions have been analyzed extensively by numerous researchers using a variety of methods and techniques [11,12,13,14,15,16,17,18]
Hadamard fractional order problems under contrasting different boundary conditions were briefly discussed in the literature [32,33,34,35,36]
Summary
The majority of the aforesaid analysis on the topic is based upon fractional differential equations and Hadamard fractional derivatives involving many numerous applications in a variety of fields such as control theory, electrical circuits, biology, physics, and finance [1,2,3,4,5,6,7,8,9,10]. Condition (ii) of Theorem 2.1 is satisfied, and L has at least one fixed point (ß , , ω ) ∈ W ∩ ( 4\ 3) i.e. the system of Hadamard fractional order boundary value problems (1)–(2) has at least one positive solution and nondecreasing solution (ß , , ω ) satisfying q ≤ ξ (ß , , ω ) with η(ß , , ω ) ≤ Q. The Hadamard fractional order BVP (1)–(2) has at least three positive solutions (ß1, 1, ω1), (ß2, 2, ω2), and (ß3, 3, ω3) such that (ß1, 1, ω1) < a, b < α(ß2, 2, ω2) and a < (ß3, 3, ω3) with α(ß3, 3, ω3) < b
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