In this article we establish a few Lyapunov-type inequalities for twopoint discrete fractional boundary value problems involving Riemann-Liouville type backward differences. To illustrate the applicability of established results, we obtain criteria for the nonexistence of nontrivial solutions and estimate lower bounds for eigenvalues of the corresponding eigenvalue problems. We also apply these inequalities to deduce criteria for the nonexistence of real zeros of certain discrete Mittag-Leffler functions.

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In this article, we present a Lyapunov-type inequality for a conformable boundary value problem associated with anti-periodic boundary conditions. To demonstrate the applicability of established result, we obtain a lower bound on the eigenvalue of the corresponding eigenvalue problem.

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PurposeAchieving a zero-carbon city requires a long-term strategic perspective. The authors propose a decision-making model which would take into account the economic, environmental and social impacts for prioritizing the zero-carbon measures for sustainable urban transportation.Design/methodology/approachAn integrated intuitionistic fuzzy gained and lost dominance score (IF-GLDS) model is introduced based on intuitionistic fuzzy Yager weighted aggregation (IFYWA) operators and proposed weight-determining IF-SPC procedure. In addition, a weighting tool is presented to obtain the weights of decision experts. Further, the feasibility and efficacy of developed IF-SPC-GLDS model is implemented on a multi-criteria investment company selection problem under IFS context.FindingsThe results of the developed model, “introducing zero-emission zones” should be considered as the first measure to implement. The preference of this initiative offers sustainable transport in India to achieve a zero-carbon transport by having the greatest impact on the modal shift from cars to sustainable mobility modes with a lower operational and implementation cost as well as having greater public support. The developed model utilized can be relocated to other smart cities which aim to achieve a zero-carbon transport. Sensitivity and comparative analyses are discussed to reveal the robustness of obtained result. The outcomes show the feasibility of the developed methodology which yields second company as the suitable choice, when compared to and validated using the other MCDA methods from the literature, including TOPSIS, COPRAS, WASPAS and CoCoSo with intuitionistic fuzzy information.Originality/valueA new intuitionistic fuzzy symmetry point of criterion (IF-SPC) approach is presented to find weights of criteria under IFSs setting. Then, an IF-GLDS model is introduced using IFYWA operators to rank the options in the realistic multi-criteria decision analysis (MCDA) procedure. For this purpose, the IFYWA operators and their properties are developed to combine the IFNs. These operators can offer a flexible way to deal with the realistic MCDA problems with IFS context.

In this article we establish a Lyapunov-type inequality for two-point Riemann-Liouville fractional boundary value problems associated with well-posed Robin boundary conditions. To illustrate the applicability of established result, we deduce criterion for the nonexistence of real zeros of a Mittag-Leffler function.

In this article, we establish a Lyapunov-type inequality for a two-point Riemann-Liouville type fractional boundary value problem associated with well-posed anti-periodic boundary conditions. As an application, we estimate a lower bound for the eigenvalue of the corresponding fractional eigenvalue problem.

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