Truncated ��-fractional Taylor’s Formula with Applications
| Autor: | SOUSA, J.V.C., OLIVEIRA, E.C. |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
multivariable truncated �� -fractional derivative
Derivada multivariada �� -fracionária truncada Matriz Jacobiana �� -fracionária truncada Truncated �� -fractional derivative truncated �� -fractional Green’s theorem Derivada parcial �� -fracionária truncada QA1-939 truncated �� -fractional Jacobian matrix Derivada �� -fracionária truncada Teorema de Green �� -fracionário truncado Mathematics truncated �� -fractional partial derivative |
| Zdroj: | TEMA, Vol 19, Iss 3, Pp 525-546 (2018) TEMA (São Carlos), Volume: 19, Issue: 3, Pages: 525-546, Published: DEC 2018 |
| ISSN: | 2179-8451 |
| Popis: | In this paper, we present and prove a new truncated �� -fractional Taylor’s formula using the truncated �� -fractional variation of constants formula. In this sense, we present the truncated �� -fractional Taylor’s remainder by means of �� -fractional integral, essential for analyzing and comparing the error, when approaching functions by polynomials. From these new results, some applications were made involving some inequalities, specifically, we generalize the Cauchy-Schwartz inequality. RESUMO Neste artigo, apresentamos e provamos uma nova fórmula de Taylor truncada por meio da fórmula �� -fracionária truncada das constantes. Neste sentido, apresentamos a formula de Taylor restante truncado por meio de integral �� -fracionária, essencial para analisar e comparar o erro, ao abordar funções por polinômios. A partir desses novos resultados, algumas aplicações foram feitas envolvendo algumas desigualdades, especificamente, generalizamos a desigualdade de Cauchy-Schwartz. |
| Databáze: | OpenAIRE |
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