Browsing by Author "Kalita, Hemanta"

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    Article
    On Generalized Local Fractal Calculus Associate With Gauge Integral and Applications
    (Vinca Inst Nuclear Sci, 2025) Kalita, Hemanta; Golmankhane, Aireza K.; Hazarika, Bipan
    In this work, a new integral so called *F alpha-integral with respect to local fractal derivatives are introduced. Several properties of *F alpha-integrals are discussed. Fundamental theorem for *F alpha-integrable functions is also introduced. A relationship ofF alpha and *F alpha integral is shown. Finally, as an application we solve fractal differential equation D alpha F[S alpha F (x)] = f[t, S alpha F (x)] with S alpha F(tau) = xi in sense of *F alpha-integral.
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    Article
    An Introduction to Fractal Lebesgue Integral
    (Walter de Gruyter GmbH, 2025) Kalita, Hemanta; Golmankhanehand, Alireza K.
    This manuscript explores various characteristics of generalized fractal measures. We expand the concept of fractal integrals in relation to step functions and examine their numerous properties. Notably, since all step functions are classified as simple functions, we apply the aforementioned generalized measure to introduce Lebesgue-type integrals, referred to as FL-integrals. Additionally, we demonstrate that all F alpha {F<^>{\alpha}} -integrable functions are FL-integrals. Lastly, we address the bounded convergence theorem within the context of fractals.