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In this paper, we derive a Mittag-Leffler function for real index and establish solutions of special type of fractional order differential equations (FDEs). The same concept is extended to discrete case by replacing polynomials into factorial polynomials and differentiation into l-difference operator. Moreover, numerical examples of our results are stated to validate our findings. The acquired results here have the ability to generate a wide range of formulas in relation to newer results. [ABSTRACT FROM AUTHOR]

In 1966, B. O'Neill [The fundamental equations of a submersion, Michigan Math. J., Volume 13, Issue 4 (1966), 459-469.] defined some fundamental equations and curvature rela- tions between the total space, the base space and the fibres on a submersion. In the present paper, we define new curvature tensors on Riemannian submersions such as Weyl projective curvature tensor, concircular curvature tensor, conharmonic curvature tensor, conformal curvature tensor and M projective curvature tensor, respectively. Finally, we obtain some results in case of the total space of Riemannian submersions has umbilical fibres for any curvature tensors mentioned by the above. [ABSTRACT FROM AUTHOR]

In this paper, we define the generalized q-Cesáro matrix by using generalized Cesáro matrix and q-Cesáro matrix. We investigate normality, self-adjointedness and Hilbert-Schmidt properties of generalized q-Cesáro matrices. [ABSTRACT FROM AUTHOR]

Goal Programming (GP), as a generalization of linear programming, is a proper technique for handling Multi-Objective Decision-Making (MODM) problems. Using this technique, we can determine multiple aspiration levels for each objective. The Neutrosophic Set (NS) theory is a powerful tool to deal with indeterminacy and inconsistent data. This paper provides a new idea to formulate Neutrosophic Multi-Choice Goal Programming (NMCGP) problems to simulate real-life situations more realistically. Also, to show the low computational complexity of the proposed model, the Space and Time complexity criteria are used in the Python language. Eventually, a practical mathematical example is solved to present the effectiveness of the proposed model. [ABSTRACT FROM AUTHOR]

This paper deal with the initial boundary value problem for a higher-order heat equation with logarithmic source term ut + (−∆)mu − ∆ut = uk−2u ln |u| . We obtain blow-up of weak solutions in the finite time, by employing potential well technique and concave technique. In addition, the upper bound of blow-up time is considered. This improves and extends some previous studies. [ABSTRACT FROM AUTHOR]