In this paper, we solve the system of functional equations f (x + y) + g(y − x) = 2f (x) g(x + y) − f (y − x) = 2g(y) and we investigate the stability of g-derivations in Banach algebras.
"In this work, we prove the Hyers–Ulam stability of hom-derivations in complex Banach algebras, associated with the additive $(s_{1}, s_{2})$-functional inequality: \begin{eqnarray}\label{0.1} \nonumber \| f(a+b) - f(a) - f(b)\| &\le& \left \|s_{1} \left(f(a+b) + f(a-b)-2f(a)\right)\right\| \\ &\quad& + \left \|s_{2} \left(2f\left( \frac{a+b}{2}\right) - f(a) - f(b)\right)\right\|, \end{eqnarray} where $s_{1}$ and $s_{2}$ are fixed nonzero complex numbers with $\sqrt{2}|s_{1}|+|s_{2}| < 1$."
The aim of the study is to discuss the controllability results of Hilfer neutral non-instantaneous impulsive fractional integro-differential equations (HNNIIFIE). Total controllability results were discussed by employing set-contraction theory and Kuratowski measure of non-compactness. Also we derived the results on optimal control using appropriate conditions. An illustration is given to validate the outcomes.
A nonclassical model known as the guava model with the conformable derivative describing the interaction of guava pests and natural enemies is studied in this paper. To this end, first the Adams–Bashforth–Moulton predictor–corrector (ABM-PC) scheme is adopted to numerically solve the guava model with the conformable derivative such that its performance is examined using the finite-difference (FD) method. The truncation error of the ABM-PC scheme is then presented in a detailed way. The effect of the order of the conformable derivative on the dynamical characteristics of guava pests and natural enemies is investigated by considering a series of graphical representations. In the end, based on the results given in this study, it is shown which day is more beneficial to harvest the guava.
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