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Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
EN In this paper we study the properties of generalized fractional derivatives (GFDs) with respect to the reflection mapping in finite intervals. We introduce symmetric and antisymmetric derivatives in a given interval and a split of arbitrary function into [J]- projections - parts with well-defined re[...]
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Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
2010 Vol. 9, nr 2 103-113
EN Two one-term nonlinear fractional differential equations with the left- or rightsided Caputo derivative are discussed. The existence and uniqueness of solutions, generated by the respective stationary function, is proved in the space of continuously differentiable function. The proof, based on the B[...]
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Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
EN Two types of one-term nonlinear fractional differential equations are considered and the existence of solutions in the space of continuous, positive and bounded below functions is proved. We transform an equation containing the left- or right-sided Caputo derivative into a fixed point condition and [...]
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Archives of Transport System Telematics
EN The paper presents laboratory studies on measuring accelerometers, which were modelled in the classical differential equations, as well as the fractional calculus. Measurement errors were examined and the classical and fractional models in terms of dynamic properties were compared. The advantages of[...]
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Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
EN In this work a numerical solution of modified Cattaneo-Vernotte equation is presented. This equation is obtained by replacing the second order time derivative by the fractional derivative in Caputo sense. In order to solve the problem with classical boundary-initial conditions, the finite difference[...]
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Archives of Civil and Mechanical Engineering
2015 Vol. 15, no. 1 231--242
EN Modern continuum mechanics needs new mathematical techniques to describe the complexity of real physical processes. Recently fractional calculus, a branch of mathematical analysis that studies differential operators of an arbitrary (real or complex) order, emerged as a powerful tool for modelling co[...]
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Bulletin of the Polish Academy of Sciences. Technical Sciences
2016 Vol. 64, nr 2 361--372
EN In this paper, a generalisation of previous author’s formulation of fractional continuum mechanics for the case of anisotropic non-locality is presented. The discussion includes a review of competitive formulations available in literature. The overall concept is based on the fractional deformation g[...]
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Journal of Applied Analysis
EN Using the Wright's generalized hypergeornetric function, we investigate a class W(q,s: A, B, λ) of analytic functions with negative coefficients. We derive many results for the modified Hadamard product of functions belonging to the class W(q,s: A, B, λ) . Moreover, we generalize some of the distort[...]
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International Journal of Applied Mathematics and Computer Science
EN Two description forms of a linear fractional-order discrete system are considered. The first one is by a fractional-order difference equation, whereas the second by a fractional-order state-space equation. In relation to the two above-mentioned description forms, stability domains are evaluated. Sev[...]
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Bulletin of the Polish Academy of Sciences. Technical Sciences
2018 Vol. 66, nr 6 991--997
EN Customized patient drug delivery overcomes classic medicine setbacks such as side effects, improper drug absorption or slow action. Nanorobots can be successfully used for targeted patient-specific drug administration, but they must be reliable in the entire circulatory system environment. This pape[...]
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Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska
2014 nr 1 44--47
PL W artykule przedstawiono wyniki badań dotyczące rozwiązań numerycznych punktowego modelu ułamkowego rzędu kinetyki neutronów oraz wymiany ciepła w reaktorze jądrowym. Zbudowano model ułamkowego rzędu z sześcioma grupami neutronów opóźnionych wraz równaniami wymiany ciepła. Model matematyczny został [...]
EN The paper presents the results concerning numerical solutions of the fractional point kinetics and heat exchange model for nuclear reactor. The fractional neutron point kinetics model with six groups of delayed neutron precursors was developed and numerical solutions were proposed. Mathematical mode[...]
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Demonstratio Mathematica
EN The object of the present paper is to investigate coefficient estimates and closure theorems for functions belonging to the class R[..] of p-valent prestarlike functions with negative coefficients. We also consider integral operators associalted with functions belonging to the class R[..]. Furthermo[...]
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International Journal of Applied Mathematics and Computer Science
EN A Haar wavelet operational matrix is applied to fractional integration, which has not been undertaken before. The Haar wavelet approximating method is used to reduce the fractional Volterra and Abel integral equations to a system of algebraic equations. A global error bound is estimated and some num[...]
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Journal of Mathematics and Applications
2010 Vol. 33 27-34
EN In this paper we are concerned with the mixed type integral inclusion [formula/wzór]. The existence of monotonic continuous solution will be proved. As an application the initial-value problem of the arbitrary (fractional) orders differential inclusion [formula/wzór] will be studied.
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Journal of Mathematics and Applications
2008 Vol. 30 5-21
EN In this paper, we investigate the various important prop-erties and characteristics of the subclasses Sn (p, q, α, β) and Cn (p, q, α, β) of multivalent functions with negative coefficients defined by using a differential operator. We also derive many results for the modified Hadamard products of fu[...]
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Archives of Transport System Telematics
EN The paper presents possibilities of using fractional calculus in dynamic measurements used in telematic equipment in cars and railway vehicles diagnostic systems. It describes a laboratory measurement system for investigating dynamic properties of accelerometers. Tests are executed in the MATLAB&Sim[...]
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International Journal of Microelectronics and Computer Science
2013 Vol. 4, nr 3 116--123
EN Fractional-order calculus offers flexible computational possibilities that can be applied to control design thereby improving industrial control loop performance. However, before theoretical results can be carried over to an industrial setting it is important to study the effects of fractional-order [...]
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Bulletin of the Polish Academy of Sciences. Technical Sciences
2018 Vol. 66, nr 4 403--410
EN The leader-following consensus problem of fractional-order multi-agent discrete-time systems with delays is considered. In the systems, interactions between agents are defined like in Krause and Cucker-Smale models, but the memory is included by taking both the fractional-order discrete-time operato[...]
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International Journal of Applied Mathematics and Computer Science
EN This paper presents a new approach to robust adaptive control, using fractional order systems as parallel feedforward in the adaptation loop. The problem is that adaptive control systems may diverge when confronted with finite sensor and actuator dynamics, or with parasitic disturbances. One of the [...]
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Przegląd Elektrotechniczny
2011 R. 87, nr 7 110-114
PL W artykule przedstawiono przykład modelowania przetwornika pomiarowego oraz rzeczywistego systemu pomiarowego za pomocą rachunku różniczkowo-całkowego ułamkowych rzędów (rachunku ułamkowego). Przedstawiono algorytm wyznaczania tych modeli zapisem ułamkowym oraz porównano ich z modelami opisanymi kla[...]
EN The paper outlines an example of modelling the measurement transducer and actual measurement system with the use of fractional calculus. The algorithm determining these models is presented in the form of a fractional calculus notation and then the models are compared to the ones described by means o[...]
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