Application of aggregated control functions for approximating C-Hilfer fractional differential equations by Safoura Rezaei Aderyani, Reza Saadati, Donal O'Regan, Fehaid Salem Alshammari

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Handbook of special functions : derivatives, integrals, series and other formulas / by 287620 Brychkov, Yury A.

Special functions : a group theoretic approach, based on lectures / by 410193 Talman, James D.

Editorial for Special Issue “Fractional Calculus and Special Functions with Applications” by Mehmet Ali Özarslan, Arran Fernandez, Iván Area

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Special Functions of Fractional Calculus in the Form of Convolution Series and Their Applications by Yuri Luchko

“…These convolution series are closely related to the general fractional integrals and derivatives with Sonine kernels and represent a new class of special functions of fractional calculus. The Mittag-Leffler functions as solutions to the fractional differential equations with the fractional derivatives of both Riemann-Liouville and Caputo types are particular cases of the convolution series generated by the Sonine kernel <inline-formula><math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>κ</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>=</mo><msup><mi>t</mi><mrow><mi>α</mi><mo>−</mo><mn>1</mn></mrow></msup><mo>/</mo><mi mathvariant="sans-serif">Γ</mi><mrow><mo>(</mo><mi>α</mi><mo>)</mo></mrow><mo>,</mo><mspace width="4pt"></mspace><mn>0</mn><mo><</mo><mi>α</mi><mo><</mo><mn>1</mn></mrow></semantics></math></inline-formula>. …”
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Higher plant calreticulins have acquired specialized functions in Arabidopsis. by Anna Christensen, Karin Svensson, Lisa Thelin, Wenjing Zhang, Nico Tintor, Daniel Prins, Norma Funke, Marek Michalak, Paul Schulze-Lefert, Yusuke Saijo, Marianne Sommarin, Susanne Widell, Staffan Persson

“…Furthermore, in planta expression, protein localization and mutant analyses revealed that the three Arabidopsis CRTs have acquired specialized functions. The AtCRT1a and CRT1b family members appear to be components of a general ER chaperone network. …”
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Mathematical mathods in engineering and physics: special functions and boundary-value problems / by 174655 Johnson, David E., Johnson, Johnny Ray

A Class of Symmetric Fractional Differential Operator Formed by Special Functions by Ibtisam Aldawish, Rabha W. Ibrahim, Suzan J. Obaiys

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On the Volterra-Type Fractional Integro-Differential Equations Pertaining to Special Functions by Yudhveer Singh, Vinod Gill, Jagdev Singh, Devendra Kumar, Kottakkaran Sooppy Nisar

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New Estimations of Hermite–Hadamard Type Integral Inequalities for Special Functions by Hijaz Ahmad, Muhammad Tariq, Soubhagya Kumar Sahoo, Jamel Baili, Clemente Cesarano

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Orthogonal Polynomials and Related Special Functions Applied in Geosciences and Engineering Computations by Vladimir Guldan, Mariana Marcokova

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Calculation of special functions arising in the problem of diffraction by a dielectric ball by Ksaverii Yu. Malyshev

“…Fuchs for Sage allows computing solutions to other linear differential equations that cannot be expressed in terms of known special functions.…”
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Hadamard-Type Inequalities for Generalized Integral Operators Containing Special Functions by Chahnyong Jung, Ghulam Farid, Muhammad Yussouf, Kamsing Nonlaopon

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The use of hermite special functions for investigation of power properties of grubbs statistics by Ludmila K Shiryaeva

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Geometric Nature of Special Functions on Domain Enclosed by Nephroid and Leminscate Curve by Reem Alzahrani, Saiful R. Mondal

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Gaussian integral by Taylor series and applications by Lázaro Lima de Sales, Jonatas Arizilanio Silva, Eliângela Paulino Bento de Souza, Hidalyn Theodory Clemente Mattos de Souza, Antonio Diego Silva Farias, Otávio Paulino Lavor

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Mathematical methods in physics : partial differential equations, fourier series, and special functions / by 403605 Henner, Victor, Belozerova, Tatyana, Forinash, Kyle

Mathematical methods in physics : partial differential equations, Fourier series, and special functions / by 403605 Henner, Victor, Belozerova, Tatyana, Forinash, Kyle

Extended incomplete Riemann-Liouville fractional integral operators and related special functions by Mehmet Ali Özarslan, Ceren Ustaoğlu

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Definite Integral of Algebraic, Exponential and Hyperbolic Functions Expressed in Terms of Special Functions by Robert Reynolds, Allan Stauffer

“…We evaluate several of these definite integrals of the form <inline-formula><math display="inline"><semantics><mrow><msubsup><mo>∫</mo><mrow><mn>0</mn></mrow><mo>∞</mo></msubsup><mfrac><mrow><msup><mrow><mo>(</mo><mi>a</mi><mo>+</mo><mi>y</mi><mo>)</mo></mrow><mi>k</mi></msup><mo>−</mo><msup><mrow><mo>(</mo><mi>a</mi><mo>−</mo><mi>y</mi><mo>)</mo></mrow><mi>k</mi></msup></mrow><mrow><msup><mi>e</mi><mrow><mi>b</mi><mi>y</mi></mrow></msup><mo>−</mo><mn>1</mn></mrow></mfrac><mi>d</mi><mi>y</mi></mrow></semantics></math></inline-formula>, <inline-formula><math display="inline"><semantics><mrow><msubsup><mo>∫</mo><mrow><mn>0</mn></mrow><mo>∞</mo></msubsup><mfrac><mrow><msup><mrow><mo>(</mo><mi>a</mi><mo>+</mo><mi>y</mi><mo>)</mo></mrow><mi>k</mi></msup><mo>−</mo><msup><mrow><mo>(</mo><mi>a</mi><mo>−</mo><mi>y</mi><mo>)</mo></mrow><mi>k</mi></msup></mrow><mrow><msup><mi>e</mi><mrow><mi>b</mi><mi>y</mi></mrow></msup><mo>+</mo><mn>1</mn></mrow></mfrac><mi>d</mi><mi>y</mi></mrow></semantics></math></inline-formula>, <inline-formula><math display="inline"><semantics><mrow><msubsup><mo>∫</mo><mrow><mn>0</mn></mrow><mo>∞</mo></msubsup><mfrac><mrow><msup><mrow><mo>(</mo><mi>a</mi><mo>+</mo><mi>y</mi><mo>)</mo></mrow><mi>k</mi></msup><mo>−</mo><msup><mrow><mo>(</mo><mi>a</mi><mo>−</mo><mi>y</mi><mo>)</mo></mrow><mi>k</mi></msup></mrow><mrow><mo form="prefix">sinh</mo><mo>(</mo><mi>b</mi><mi>y</mi><mo>)</mo></mrow></mfrac><mi>d</mi><mi>y</mi></mrow></semantics></math></inline-formula> and <inline-formula><math display="inline"><semantics><mrow><msubsup><mo>∫</mo><mrow><mn>0</mn></mrow><mo>∞</mo></msubsup><mfrac><mrow><msup><mrow><mo>(</mo><mi>a</mi><mo>+</mo><mi>y</mi><mo>)</mo></mrow><mi>k</mi></msup><mo>+</mo><msup><mrow><mo>(</mo><mi>a</mi><mo>−</mo><mi>y</mi><mo>)</mo></mrow><mi>k</mi></msup></mrow><mrow><mo form="prefix">cosh</mo><mo>(</mo><mi>b</mi><mi>y</mi><mo>)</mo></mrow></mfrac><mi>d</mi><mi>y</mi></mrow></semantics></math></inline-formula> in terms of a special function where <i>k</i>, <i>a</i> and <i>b</i> are arbitrary complex numbers.…”
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