We apply some fixed point principles and Leray-Schauder degree theory to obtain the main results.
Next, we will apply some fixed point theorems to study the existence and uniqueness results of this generalized fractional boundary value problem.
Different from the literature mentioned above, in the present paper, the authors apply some fixed point theorems for differentiable operators to establish the existence results on positive solutions to the fractional nonlocal boundary value problem (1.1 - 1.2 1.1 - 1.2
Since the present author has studied the fixed point theory on posets for several years and has made some applications to Nash equilibrium problems, so, in this paper, we will apply some fixed point theorems on posets to study the solvability of split Nash equilibrium problems for dual games.
The new model was established by integrating experimental information and knowledge not included in Shinto's model (section "Methods"), and we applied some optimization methods to fix the unknown parameters introduced by integrating these information and knowledge.
By applying some standard fixed point principles, some existence and uniqueness results are obtained.
In Section 4, by applying some standard fixed point principles, we verify the existence of solutions for problem (1.1 - 1.3 1.1 - 1.3
By applying some standard fixed point theorems, we obtain the sufficient conditions for the existence and uniqueness of solutions of the problem at hand.
By applying some standard fixed point theorems, Agarwal et al. [34] and Ahmad et al. [35] showed some existence results for sequential q-fractional integrodifferential equations with q-antiperiodic boundary conditions and nonlocal four-point boundary conditions, respectively.
We prove the existence and uniqueness of solutions for nonlinear integro-differential equations of fractional order with three-point nonlocal fractional boundary conditions by applying some standard fixed point theorems.
In a more recent work [49], the authors presented a novel idea of unification of anti-periodic and multipoint boundary conditions and developed the existence theory for sequential fractional differential equations by applying some standard fixed point theorems due to Banach, Krasnoselskii, Leray-Schauder alternative criterion, and Leray-Schauder degree theory.
