Applications of I-function in solving fractional differential equations and boundary value problems
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Published:
Apr 1, 2025
Keywords:
I-functions, Polynomials, Mathematical, Fractional Integral, Fractional Calculus
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Abstract
An extension of the famous H-function by Fox, the I-function, which in turn extends to the incomplete I-functions. Solving the one-dimensional heat flow problem using incomplete I-functions is the focus of this work. Additionally, we derive a large number of special situations from our primary conclusions. The Struve's function with its enlarged integral with the I-function in two variables is a generic class of polynomials. This study also addressed a boundary value problem concerning the steady-state temperature distribution of a rectangular plate by using the I-function, Struve's function, and the Extended General Class of Polynomials.
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- Mishra, Jyoti. (2018). A remark on fractional differential equation involving I-function. The European Physical Journal Plus. 133. 10.1140/epjp/i2018-11897-y.
- Shiri, Babak & Baleanu, Dumitru. (2019). System of fractional differential algebraic equations with applications. Chaos Solitons & Fractals. 120. 203-212. 10.1016/j.chaos.2019.01.028.
- Bansal, Manish & Lal, Shiv & Kumar, Devendra & Kumar, Dr. Sunil & Singh, Jagdev. (2020). Fractional differential equation pertaining to an integral operator involving incomplete H‐function in the kernel. Mathematical Methods in the Applied Sciences. 47. 10.1002/mma.6670.
- Tidke, Haribhau & Patil, Gajanan. (2022). Some Results on Fractional Differential Equation With Mixed Boundary Condition via S-Iteration. Communications in Mathematics and Applications. 13. 507-527. 10.26713/cma. v13i2.1802.
- Wang, Youyu & Liang, Shuilian & Wang, Qichao. (2018). Existence results for fractional differential equations with integral and multi-point boundary conditions. Boundary Value Problems. 2018. 10.1186/s13661-017-0924-4.
- Manilal shah., On some applications related to Fox’s H-function of two variables, publications De l’InstituteMathematique, Novelle series tome 16(30), (1973), pp. 123-133
- Neelampandey and Jyothi Mishra., I-functin and boundary value problem in a rectangular plate, Research Journal of Mathematical and Statistical science, 2(10), (2014), pp. 5-7
- Pragathi Kumar Y, AlemMabrathu, Purnima B.V and Satyanarayana B., Mellin and Laplace Transform involving the product of general class of polynomials and I-function of two variables, International J. Math .Sci. &Engg. App., 10(III), (2016), pp. 143-150
- Satyanarayana B., Purnima B.V., Pragathi Kumar Y., Solution of Boundary Value Problem Involving Struve’s Function and I-Function of Two Variables, Jour of Advanced Research in Dynamical & Control Systems, Vol. 10, 10-Special Issue, 2018, pp. 57-63
- Shantha Kumari K, Vasudevan Nambisan T.M and Rathie Arjun K., A Study of I-function of two variables, Le Mathematiche, 69(1), (2012), pp. 25-305
- Sharma, C.K.., Mishra, P.L., On the I-function of two variables and its certain properties, ACI, 17(1991), 1-4.
- Singh, Y., Joshi, L., On some double integrals involving H -function of two variables and spheroidal functions, Int. J. Compt. Tech. 12(1),(2013), 358-366.
- Srivastava, S.S., Singh, A., Temperature in the Prism involving I-function of two variables, Ultra Scientist, Vol. 25(1)A, 2013, 207-209.
- Yashwant Singh, Nanda Kulkarni, A boundary value problem and Expansion formula of I-function and general class of polynomials with Applications. Int. journal of Engineering Research and Applications, Vol-5, Issue 1 (part3), January 2015, pp. 105-110
- Yashwant Singh and Nanda Kulkarni, Some Expansion Formulae for the H -function, Advances in Theoretical and Applied Mathematics, V.12, No. 2(2017), pp.65-69.