Search results for: RIGHT-HANDED RIEMANN-LIOUVILLE FRACTIONAL DERIVATIVES - Bridge of Knowledge

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Search results for: RIGHT-HANDED RIEMANN-LIOUVILLE FRACTIONAL DERIVATIVES

  • Fractional Problems with Right-Handed Riemann-Liouville Fractional Derivatives

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    In this paper, we investigate the existence of solutions for advanced fractional differential equations containing the right-handed Riemann-Liouville fractional derivative both with nonlinear boundary conditions and also with initial conditions given at the end point T of interval [0,T ]. We use both the method of successive approximations, the Banach fixed point theorem and the monotone iterative technique, as well. Linear problems...

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  • Comments on various extensions of the Riemann–Liouville fractional derivatives : About the Leibniz and chain rule properties

    Starting from the Riemann–Liouville derivative, many authors have built their own notion of fractional derivative in order to avoid some classical difficulties like a non zero derivative for a constant function or a rather complicated analogue of the Leibniz relation. Discussing in full generality the existence of such operator over continuous functions, we derive some obstruction Lemma which can be used to prove the triviality...

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  • Systems of Nonlinear Fractional Differential Equations

    Using the iterative method, this paper investigates the existence of a unique solution to systems of nonlinear fractional differential equations, which involve the right-handed Riemann-Liouville fractional derivatives D(T)(q)x and D(T)(q)y. Systems of linear fractional differential equations are also discussed. Two examples are added to illustrate the results.

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  • On Applications of Fractional Derivatives in Electromagnetic Theory

    Publication

    - Year 2020

    In this paper, concepts of fractional-order (FO) derivatives are analysed from the point of view of applications in the electromagnetic theory. The mathematical problems related to the FO generalization of Maxwell's equations are investigated. The most popular formulations of the fractional derivatives, i.e., Riemann-Liouville, Caputo, Grünwald-Letnikov and Marchaud definitions, are considered. Properties of these derivatives are...

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  • On Applications of Fractional Derivatives in Circuit Theory

    Publication

    - Year 2020

    In this paper, concepts of fractional-order (FO) derivatives are discussed from the point of view of applications in the circuit theory. The properties of FO derivatives required for the circuit-level modelling are formulated. Potential problems related to the generalization of transmission line equations with the use of FO derivatives are presented. It is demonstrated that some of formulations of the FO derivatives have limited...

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