Numerical Solutions of Coupled Systems of Fractional Order Partial Differential Equations

We develop a numerical method by using operational matrices of fractional order integrations and differentiations to obtain approximate solutions to a class of coupled systems of fractional order partial differential equations (FPDEs). We use shifted Legendre polynomials in two variables. With the help of the aforesaid matrices, we convert the system under consideration to a system of easily solvable algebraic equation of Sylvester type. During this process, we need no discretization of the data. We also provide error analysis and some test problems to demonstrate the established technique

Existence Theory of Differential Equations of Arbitrary Order

The aims of this chapter are devoted to investigate a system of fractional-order differential equations (FDEs) with multipoint boundary conditions. Necessary and sufficient conditions are investigated for at most one solution to the proposed problem. Also, results for the existence of at least one or two positive solutions are developed by using a fixed-point theorem of concave-type operator for the considered problem. Further, we extend the conditions for more than two solutions and established some adequate conditions for multiplicity results to the proposed problem. Also, a result devoted to Hyers-Ulam stability is discussed. Suitable examples are provided to verify the established results

A new Hilbert-type integral inequality and the equivalent form

We give a new Hilbert-type integral inequality with the best constant factor by estimating the weight function. And the equivalent form is considered

Editorial: Social cognition and mental health among children and youth

This editorial comment on “Social cognition and mental health among children and youth” aims to provide a forum to improve research in this field and its contribution to health psychology, the understanding of risk and protective factors, and the exploration of innovative psychosocial interventions to benefit children and youth's health and wellbeing. People's feelings and social experiences are very influenced by their social, cultural, educational and autobiographical contexts. Nota: Parte de texto retirado do corpo do artigo.info:eu-repo/semantics/publishedVersio