Operational Solution of Non-Integer Ordinary and Evolution-Type Partial Differential Equations

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dc.contributor.authorZhukovsky, Konstantin V.
dc.contributor.authorSrivastava, H.M.
dc.date.accessioned2018-12-19T05:52:21Z
dc.date.available2018-12-19T05:52:21Z
dc.date.copyright2016en_US
dc.date.issued2016
dc.description.abstractA method for the solution of linear differential equations (DE) of non-integer order and of partial differential equations (PDE) by means of inverse differential operators is proposed. The solutions of non-integer order ordinary differential equations are obtained with recourse to the integral transforms and the exponent operators. The generalized forms of Laguerre and Hermite orthogonal polynomials as members of more general Appèl polynomial family are used to find the solutions. Operational definitions of these polynomials are used in the context of the operational approach. Special functions are employed to write solutions of DE in convolution form. Some linear partial differential equations (PDE) are also explored by the operational method. The Schrödinger and the Black–Scholes-like evolution equations and solved with the help of the operational technique. Examples of the solution of DE of non-integer order and of PDE are considered with various initial functions, such as polynomial, exponential, and their combinations.en_US
dc.description.reviewstatusRevieweden_US
dc.description.scholarlevelFacultyen_US
dc.identifier.citationZhukovsky, K.V. & Srivastava, H.M. (2016). Operational Solution of Non-Integer Ordinary and Evolution-Type Partial Differential Equations. Axioms, 5(4), 29. https://doi.org/10.3390/axioms5040029en_US
dc.identifier.urihttps://doi.org/10.3390/axioms5040029
dc.identifier.urihttp://hdl.handle.net/1828/10427
dc.language.isoenen_US
dc.publisherAxiomsen_US
dc.subjectinverse operator
dc.subjectderivative
dc.subjectdifferential equation
dc.subjectspecial functions
dc.subjectHermite and Laguerre polynomials
dc.subject.departmentDepartment of Mathematics and Statistics
dc.titleOperational Solution of Non-Integer Ordinary and Evolution-Type Partial Differential Equationsen_US
dc.typeArticleen_US

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