The increasing global demand for energy, environmental concerns, and rapid technological advancements have made future energy planning a challenging multi-criteria decision-making (MCDM) problem. The selection of appropriate energy strategies requires simultaneously considering economic, environmental, technological, and policy-related factors under uncertain and evolving conditions. Conventional MCDM approaches are often inadequate for handling complex uncertainty and temporal variations in decision information. To address these challenges, this study proposes a Temporal-Aware Complex q-Rung Orthopair Fuzzy Aczel–Alsina CRITIC-WASPAS (Cq-ROF-AA-CRITIC-WASPAS) framework for future energy planning. The proposed framework employs Cq-ROFSs to represent uncertain decision information, while the proposed Aczel–Alsina aggregation operators effectively fuse temporal decision matrices by assigning greater importance to recent evaluations. The Criteria Importance Through Intercriteria Correlation (CRITIC) method objectively determines attribute weights by considering contrast intensity and inter-criteria correlation, whereas the Weighted Aggregated Sum Product Assessment (WASPAS) method ranks the energy alternatives through a hybrid additive-multiplicative evaluation strategy. A hypothetical future energy planning case study is presented to demonstrate the applicability of the proposed mathematical model using evaluation criteria related to economic viability, environmental sustainability, technological preparedness, energy security, and policy flexibility. Furthermore, comparative and sensitivity analyses are conducted to evaluate the effectiveness and stability of the proposed framework. The obtained results demonstrate that the proposed framework provides a flexible and systematic approach for handling complex uncertainty and temporal decision information, offering reliable decision support for future energy planning and other uncertain MCDM applications.
Linear-quadratic (LQ) optimal control problems have been widely studied under symmetric information and regularity assumptions. However, in many practical systems, multiple controllers operate with different information sets, and the standard regularity condition may fail due to singular weighting matrices. This paper investigates a stochastic irregular LQ optimal control problem with dual controllers and two-layer asymmetric partial observations, in which one controller has strictly less information than the other. The main contribution is the derivation of both the solvability conditions and the explicit feedback-form solutions for this problem. To this end, we reformulate the optimization problem as a system of forward-backward stochastic differential equations (FBSDEs) that naturally captures the asymmetric information structure. By solving these FBSDEs via four interconnected Riccati equations, we obtain explicit optimal controllers for both the regular and irregular cases. In the irregular case, where the standard Riccati equation is not directly solvable, we introduce auxiliary Riccati equations and derive additional existence conditions involving singular matrix decompositions. A detailed technical comparison with existing results confirms that our solution is not a straightforward extension, as prior works either addressed irregular LQ control under full information or asymmetric information under regular conditions. This work provides a unified framework for optimal control problems where information asymmetry and singularity arise simultaneously.
This work puts forward a family of operators, which we term enriched ∇-preserving contractions, acting on a normed space carrying an arbitrary binary relation ∇. The family gathers several familiar classes under one roof: Banach contractions, order-theoretic contractions, and certain nonexpansive maps, among them averaged maps whose fixed points lie beyond the reach of ordinary contraction arguments; all arise through suitable choices of the constants and of the relation. Working in this relational framework, we show that any such operator admits a fixed point, even though its defining contractive estimate is demanded only on ∇-related pairs rather than across the whole space. A device used repeatedly is the symmetry of the norm: it forces ∇ and its symmetric closure to act compatibly with the operator, and this is what keeps the fixed-point conclusions meaningful. The fixed points themselves are located through the Krasnoselskii iteration, and a path criterion formulated in the symmetric closure of ∇ then yields their uniqueness; an almost contraction variant of the scheme is treated as well. By way of application, the theory settles the solvability, and under the stated hypotheses the uniqueness, of solutions to a Caputo fractional boundary value problem with an integral condition and to a nonlinear matrix equation. Numerical experiments over several groups of Lipschitz coefficients confirm the convergence threshold predicted by the theory, and the iteration is compared with Riemann-Hilbert analysis, Lie group integrators, physics-informed neural networks, and neural symbolic derivation tools, so that strengths and limits of the framework can be judged objectively.
The notion of a double controlled metric type space was introduced by Abdeljawad et al. as a broadening of the controlled metric type spaces of Mlaiki et al., and shortly afterwards Aydi et al. formulated the new extended b-metric spaces to widen the extended b-metric spaces of Kamran et al. Building on these developments, the present work advances the class of (θ, α)-metric spaces, a structure that simultaneously subsumes b-metric spaces, new extended b-metric spaces, controlled metric type spaces and double controlled metric type spaces. This is accomplished by attaching two control functions θ(ζ, µ, s) and α(ζ, µ, s) to the terms situated on the right-hand side of the triangle inequality in the axioms defining a (θ, α)-metric space. We first prove, through explicit propositions, that each of the aforementioned structures is recovered as a special case under an appropriate choice of θ and α, and we supply non-trivial examples confirming that the new class is strictly broader than a b-metric space. Within this setting, a collection of fixed point theorems is derived for φ-contractive and Reich–Ćirić–Rus–type operators, together with their corollaries. Finally, two applications are presented: the principal theorem is first used to guarantee that a nonlinear algebraic equation possesses a unique solution, and it is then applied to establish the existence and uniqueness of a solution to a nonlinear Caputo fractional boundary value problem, thereby strengthening the connection of the theory with differential equations.
We introduce two classes of operators on normed spaces, the enriched polynomial contractions and the almost enriched polynomial contractions. Both classes contain the enriched contractions of Berinde and Păcurar and the polynomial-type contractions of Jleli, Pacurar and Samet as special cases. In Banach spaces, we prove existence, uniqueness, and convergence theorems for the fixed points, first under continuity of the operator and then under the weaker assumption of Picard continuity, with the fixed points approximated by Krasnoselskii-type iteration. Several classical results, including the Banach contraction principle and the enriched contraction theorem, are recovered as special cases, and several worked examples are given. As the main application, we consider a nonlinear Caputo fractional boundary value problem of order 2 < N ≤ 3. Writing it as a fixed-point equation and assuming an explicit Lipschitz condition, we prove that it has a unique solution. We then examine the constructive side of this result numerically: on a manufactured problem with a known exact solution, we run the associated fractional-quadrature Krasnoselskii iteration, check that its measured geometric rate stays below the certified contraction factor, and recover the same solution with a neural fixed-point solver, a network trained to satisfy the discretized fixed-point equation of the same operator, and we relate the accuracy of both solvers to the underlying quadrature error. The numerical results are consistent with the theory and illustrate its use on a class of nonlinear fractional models of this form.
