Some fractional calculus findings associated with the product of incomplete ℵ-function and Srivastava polynomials

[1]Bagley R.L., Torvik P.J., A theoretical basis for the application of fractional calculus to viscoelasticity, Journal of Rheology, 27(3), 201–210, 1983. BagleyR.L. TorvikP.J. A theoretical basis for the application of fractional calculus to viscoelasticity Journal of Rheology 27 3 201 210 1983 Search in Google Scholar

[2]Fellah Z.E.A., Depollier C., Fellah M., Application of fractional calculus to the sound waves propagation in rigid porous materials: validation via ultrasonic measurements, Acta Acustica United with Acustica, 88(1), 34–39, 2002. FellahZ.E.A. DepollierC. FellahM. Application of fractional calculus to the sound waves propagation in rigid porous materials: validation via ultrasonic measurements Acta Acustica United with Acustica 88 1 34 39 2002 Search in Google Scholar

[3]Rossikhin Y.A., Shitikova M.V., Application of fractional calculus for dynamic problems of solid mechanics: novel trends and recent results, Applied Mechanics Reviews, 63(1), 010801, 2010. RossikhinY.A. ShitikovaM.V. Application of fractional calculus for dynamic problems of solid mechanics: novel trends and recent results Applied Mechanics Reviews 63 1 010801 2010 Search in Google Scholar

[4]Sun Y., Zheng C., Fractional-order modelling of state-dependent non-associated behaviour of soil without using state variable and plastic potential, Advances in Difference Equations, 2019(1), 83, 2019. SunY. ZhengC. Fractional-order modelling of state-dependent non-associated behaviour of soil without using state variable and plastic potential Advances in Difference Equations 2019 1 83 2019 Search in Google Scholar

[5]Ata E., Kıymaz İ.O., Generalized gamma, beta and hypergeometric functions defined by wright function and applications to fractional differential equations, Cumhuriyet Science Journal, 43(4), 684–695, 2022. AtaE. Kıymazİ.O. Generalized gamma, beta and hypergeometric functions defined by wright function and applications to fractional differential equations Cumhuriyet Science Journal 43 4 684 695 2022 Search in Google Scholar

[6]Magin R.L., Fractional calculus in bioengineering: Part 2, Critical Reviews in Biomedical Engineering, 32(2), 105–194, 2004. MaginR.L. Fractional calculus in bioengineering: Part 2 Critical Reviews in Biomedical Engineering 32 2 105 194 2004 Search in Google Scholar

[7]Ata E., M-Lauricella hypergeometric functions: integral representations and solutions of fractional differential equations, Communications Faculty of Sciences University of Ankara Series, A1 Mathematics and Statistics, 72(2), 512–529, 2023. AtaE. M-Lauricella hypergeometric functions: integral representations and solutions of fractional differential equations Communications Faculty of Sciences University of Ankara Series, A1 Mathematics and Statistics 72 2 512 529 2023 Search in Google Scholar

[8]Srivastava H.M., Saxena R.K., Operators of fractional integration and their applications, Applied Mathematics and Computation, 118(1), 1–52, 2001. SrivastavaH.M. SaxenaR.K. Operators of fractional integration and their applications Applied Mathematics and Computation 118 1 1 52 2001 Search in Google Scholar

[9]Debnath L., Bhatta D., Integral Transforms and Their Applications, (Third Ed.), Chapman and Hall (CRC Press), Taylor and Francis Group, London and New York, USA, 2015. DebnathL. BhattaD. Integral Transforms and Their Applications Third Ed. Chapman and Hall (CRC Press), Taylor and Francis Group London and New York, USA 2015 Search in Google Scholar

[10]Saigo M., A remark on integral operators involving the Gauss hypergeometric functions, Mathematical Reports of College of General Education, Kyushu University, 11(2), 135–143, 1978. SaigoM. A remark on integral operators involving the Gauss hypergeometric functions Mathematical Reports of College of General Education, Kyushu University 11 2 135 143 1978 Search in Google Scholar

[11]Samko S.G., Kilbas A.A., Marichev O.I., Fractional Integrals and Derivatives: Theory and Applications; Gordon and Breach: Yverdon, Switzerland, 1993. SamkoS.G. KilbasA.A. MarichevO.I. Fractional Integrals and Derivatives: Theory and Applications Gordon and Breach Yverdon, Switzerland 1993 Search in Google Scholar

[12]Miller K.S., Ross B., An Introduction to Fractional Calculus and Fractional Differential Equations, Wiley, New York, USA, 1993. MillerK.S. RossB. An Introduction to Fractional Calculus and Fractional Differential Equations Wiley New York, USA 1993 Search in Google Scholar

[13]Jangid K., Bhatter S., Meena S., Baleanu D., Al-Qurashi M., Purohit S.D., Some fractional calculus findings associated with the incomplete I-functions, Advances in Difference Equations, 2020(1), 265, 2020. JangidK. BhatterS. MeenaS. BaleanuD. Al-QurashiM. PurohitS.D. Some fractional calculus findings associated with the incomplete I-functions Advances in Difference Equations 2020 1 265 2020 Search in Google Scholar

[14]Love E.R., Some integral equations involving hypergeometric functions, Proceedings of the Edinburgh Mathematical Society, 15(3), 169–198, 1967. LoveE.R. Some integral equations involving hypergeometric functions Proceedings of the Edinburgh Mathematical Society 15 3 169 198 1967 Search in Google Scholar

[15]Ram J., Kumar D., Generalized fractional integration of the ℵ-function, Journal of Rajasthan Academy of Physical Sciences, 10(4), 373–382, 2011. RamJ. KumarD. Generalized fractional integration of the ℵ-function Journal of Rajasthan Academy of Physical Sciences 10 4 373 382 2011 Search in Google Scholar

[16]Chaudhry M.A., Zubair S.M., Generalized incomplete gamma functions with applications, Journal of Computational and Applied Mathematics, 55(1), 99–124, 1994. ChaudhryM.A. ZubairS.M. Generalized incomplete gamma functions with applications Journal of Computational and Applied Mathematics 55 1 99 124 1994 Search in Google Scholar

[17]Srivastava H.M., Singh N.P., The integration of certain products of the multivariable H-function with a general class of polynomials, Rendiconti del Circolo Matematico di Palermo, 32(2), 157–187, 1983. SrivastavaH.M. SinghN.P. The integration of certain products of the multivariable H-function with a general class of polynomials Rendiconti del Circolo Matematico di Palermo 32 2 157 187 1983 Search in Google Scholar

[18]Bhatter S., Nishant, Suthar D.L., Purohit S.D., Boros integral involving the product of family of polynomials and the incomplete I-function, Journal of Computational Analysis and Applications, 31(3), 400–412, 2023. BhatterS. Nishant SutharD.L. PurohitS.D. Boros integral involving the product of family of polynomials and the incomplete I-function Journal of Computational Analysis and Applications 31 3 400 412 2023 Search in Google Scholar

[19]Marichev O.I., Volterra equation of Mellin convolution type with a Horn function in the kernel, Izvestiya Akademii Nauk Belarusi. Seriya Fiziko-Matematicheskikh Nauk, 1, 128–129, 1974. MarichevO.I. Volterra equation of Mellin convolution type with a Horn function in the kernel, Izvestiya Akademii Nauk Belarusi Seriya Fiziko-Matematicheskikh Nauk 1 128 129 1974 Search in Google Scholar

[20]Saigo M., Maeda N., More Generalization of Fractional Calculus, In Transform Methods and Special Functions, Varna’96 Edited by Rusev P., Dimovski I., Kiryakova V., (Proc. Second Internat. Workshop), Science Culture Technology Publishing: Singapore, 386–400, 1998. SaigoM. MaedaN. More Generalization of Fractional Calculus In Transform Methods and Special Functions, Varna’96 Edited by RusevP. DimovskiI. KiryakovaV. (Proc. Second Internat. Workshop), Science Culture Technology Publishing Singapore 386 400 1998 Search in Google Scholar

[21]Baleanu D., Kumar D., Purohit S.D., Generalized fractional integrals of product of two H-functions and a general class of polynomials, International Journal of Computer Mathematics, 93(8), 1320–1329, 2016. BaleanuD. KumarD. PurohitS.D. Generalized fractional integrals of product of two H-functions and a general class of polynomials International Journal of Computer Mathematics 93 8 1320 1329 2016 Search in Google Scholar

[22]Purohit S.D., Suthar D.L., Kalla S.L., Marichev-Saigo-Maeda fractional integration operators of the Bassel functions, Le Matematiche, 67(1), 21–32, 2012. PurohitS.D. SutharD.L. KallaS.L. Marichev-Saigo-Maeda fractional integration operators of the Bassel functions Le Matematiche 67 1 21 32 2012 Search in Google Scholar

[23]Kilbas A.A., Srivastava H.M., Trujillo J.J., Theory and Applications of Fractional Differential Equations, North-Holland Mathematical Studies, Elsevier, New York, USA, (1st Ed.) 204, USA, 2006. KilbasA.A. SrivastavaH.M. TrujilloJ.J. Theory and Applications of Fractional Differential Equations, North-Holland Mathematical Studies Elsevier New York, USA 1st Ed. 204 USA 2006 Search in Google Scholar

[24]Bansal M.K., Kumar D., Nisar K.S., Singh J., Certain fractional calculus and integral transform results of incomplete ℵ-functions with applications, Mathematical Methods in the Applied Sciences, 43(8), 5602–5614, 2020. BansalM.K. KumarD. NisarK.S. SinghJ. Certain fractional calculus and integral transform results of incomplete ℵ-functions with applications Mathematical Methods in the Applied Sciences 43 8 5602 5614 2020 Search in Google Scholar

[25]Bhatter S., Nishant, Shyamsunder, Mathematical model on the effects of environmental pollution on biological populations, Advances in Mathematical Modelling, Applied Analysis and Computation, ICMMAAC 2022, Springer, 666, 488–496, 2023. BhatterS. Nishant Shyamsunder Mathematical model on the effects of environmental pollution on biological populations, Advances in Mathematical Modelling Applied Analysis and Computation, ICMMAAC 2022, Springer 666 488 496 2023 Search in Google Scholar

[26]Südland N., Baumann G., Nonnenmacher T.F., Fractional driftless Fokker-Planck equation with power law diffusion coefficients, Computer Algebra in Scientific Computing CASC 2001, Proceedings of the Fourth International Workshop on Computer Algebra in Scientific Computing, Konstanz, Springer Berlin Heidelberg, Germany, 513–528, 2001. SüdlandN. BaumannG. NonnenmacherT.F. Fractional driftless Fokker-Planck equation with power law diffusion coefficients, Computer Algebra in Scientific Computing CASC 2001 Proceedings of the Fourth International Workshop on Computer Algebra in Scientific Computing Konstanz, Springer Berlin Heidelberg, Germany 513 528 2001 Search in Google Scholar

[27]Südland N., Baumann G., Nonnenmacher T.F., Open problem: who knows about the ℵ-function?, Fractional Calculus and Applied Analysis, 1(4), 401–402, 1998. SüdlandN. BaumannG. NonnenmacherT.F. Open problem: who knows about the ℵ-function? Fractional Calculus and Applied Analysis 1 4 401 402 1998 Search in Google Scholar

[28]Bansal M.K., Kumar D., On the integral operators pertaining to a family of incomplete I-functions, AIMS Mathematics, 5(2), 1247–1259, 2020. BansalM.K. KumarD. On the integral operators pertaining to a family of incomplete I-functions AIMS Mathematics 5 2 1247 1259 2020 Search in Google Scholar

[29]Saxena V.P., Formal solution of certain new pair of dual integral equations involving H-functions, Proceedings of the National Academy of Sciences, India Section A: Physical Sciences, 52, 366–375, 1982. SaxenaV.P. Formal solution of certain new pair of dual integral equations involving H-functions Proceedings of the National Academy of Sciences, India Section A: Physical Sciences 52 366 375 1982 Search in Google Scholar

[30]Jangid K., Bhatter S., Meena S., Purohit S.D., Certain classes of the incomplete I-functions and their properties, Discontinuity Nonlinearity and Complexity, 12(2), 437–454, 2023. JangidK. BhatterS. MeenaS. PurohitS.D. Certain classes of the incomplete I-functions and their properties Discontinuity Nonlinearity and Complexity 12 2 437 454 2023 Search in Google Scholar

[31]Jangid K., Purohit S.D., Agarwal R., Agarwal R.P., On the generalization of fractional kinetic equation comprising incomplete H-function, Kragujevac Journal of Mathematics, 47(5), 701–712, 2023. JangidK. PurohitS.D. AgarwalR. AgarwalR.P. On the generalization of fractional kinetic equation comprising incomplete H-function Kragujevac Journal of Mathematics 47 5 701 712 2023 Search in Google Scholar

[32]Srivastava H.M., Chaudhry M.A., Agarwal R.P., The incomplete Pochhammer symbols and their applications to hypergeometric and related functions, Integral Transforms and Special Functions, 23(9), 659–683, 2012. SrivastavaH.M. ChaudhryM.A. AgarwalR.P. The incomplete Pochhammer symbols and their applications to hypergeometric and related functions Integral Transforms and Special Functions 23 9 659 683 2012 Search in Google Scholar

[33]Srivastava H.M., Gupta K.C., Goyal S.P., The H-functions of One and Two Variables with Applications, New Delhi and Madras, South Asian Publishers, India, 1982. SrivastavaH.M. GuptaK.C. GoyalS.P. The H-functions of One and Two Variables with Applications New Delhi and Madras, South Asian Publishers India 1982 Search in Google Scholar

[34]Srivastava H.M., Saxena R.K., Parmar R.K., Some families of the incomplete H-functions and the incomplete H-functions and associated integral transforms and operators of fractional calculus with applications, Russian Journal of Mathematical Physics, 25(1), 116–138, 2018. SrivastavaH.M. SaxenaR.K. ParmarR.K. Some families of the incomplete H-functions and the incomplete H-functions and associated integral transforms and operators of fractional calculus with applications Russian Journal of Mathematical Physics 25 1 116 138 2018 Search in Google Scholar

[35]Saxena R.K., Saigo M., Generalized fractional calculus of the H-function associated with the Appell function F₃, Journal of Fractional Calculus, 19, 89–104, 2001. SaxenaR.K. SaigoM. Generalized fractional calculus of the H-function associated with the Appell function F₃ Journal of Fractional Calculus 19 89 104 2001 Search in Google Scholar

[36]Saxena R.K., Generalized fractional calculus of the ℵ-function involving a general class of polynomials, Acta Mathematica Scientia, 35(5), 1095–1110, 2015. SaxenaR.K. Generalized fractional calculus of the ℵ-function involving a general class of polynomials Acta Mathematica Scientia 35 5 1095 1110 2015 Search in Google Scholar

[37]Saxena R.K., Ram J., Kumar D., Generalized fractional differentiation of the ℵ-function associated with the Appell function F₃, Acta Ciencia Indica, 38(4), 781–792, 2012. SaxenaR.K. RamJ. KumarD. Generalized fractional differentiation of the ℵ-function associated with the Appell function F₃ Acta Ciencia Indica 38 4 781 792 2012 Search in Google Scholar

[38]Ata E., Kıymaz İ.O., A study on certain properties of generalized special functions defined by Fox-Wright function, Applied Mathematics and Nonlinear Sciences, 5(1), 147–162, 2020. AtaE. Kıymazİ.O. A study on certain properties of generalized special functions defined by Fox-Wright function Applied Mathematics and Nonlinear Sciences 5 1 147 162 2020 Search in Google Scholar

[39]Chaudhry M.A., Qadir A., Srivastava H.M., Paris R.B., Extended hypergeometric and confluent hypergeometric functions, Applied Mathematics and Computation, 159(2), 589–602, 2004. ChaudhryM.A. QadirA. SrivastavaH.M. ParisR.B. Extended hypergeometric and confluent hypergeometric functions Applied Mathematics and Computation 159 2 589 602 2004 Search in Google Scholar

[40]Srivastava H.M., Agarwal P., Jain S., Generating functions for the generalized Gauss hypergeometric functions, Applied Mathematics and Computation, 247, 348–352, 2014. SrivastavaH.M. AgarwalP. JainS. Generating functions for the generalized Gauss hypergeometric functions Applied Mathematics and Computation 247 348 352 2014 Search in Google Scholar