Fractional differential equations related to an integral operator involving the incomplete \(I\)-function as a kernel. (English) Zbl 1533.34009
MSC:
| 34A08 | Fractional ordinary differential equations |
| 34B10 | Nonlocal and multipoint boundary value problems for ordinary differential equations |
| 33C60 | Hypergeometric integrals and functions defined by them (\(E\), \(G\), \(H\) and \(I\) functions) |
| 44A10 | Laplace transform |
References:
| [1] | S.Kumawat, S.Bhatter, D. L.Suthar, S. D.Purohit, and K.Jangid, Numerical modeling on age‐based study of coronavirus transmission, Appl. Math. Sci. Eng. (AMSE)30 (2022), no. 1, 609-634. |
| [2] | A. M.Mishra, S. D.Purohit, K. M.Owolabi, and Y. D.Sharma, A nonlinear epidemiological model considering asymptotic and quarantine classes for SARS CoV‐2 virus, Chaos, Solitons Fract.138 (2020), 109953. · Zbl 1490.92108 |
| [3] | Shyamsunder, S.Bhatter, K.Jangid, A.Abidemi, K. M.Owolabi, and S. D.Purohit, A new fractional mathematical model to study the impact of vaccination on Covid‐19 outbreaks, Decision Anal. J.6 (2023), 100156. |
| [4] | W.Gao, P.Veeresha, C.Cattani, C.Baishya, and H. M.Baskonus, Modified predictor-corrector method for the numerical solution of a fractional‐order sir model with 2019‐NCOV, Fract. Fract.6 (2022), no. 2, 92. |
| [5] | Shyamsunder, S.Bhatter, K.Jangid, and S. D.Purohit, Fractionalized mathematical models for drug diffusion, Chaos Solitons Fract.165 (2022), 112810. |
| [6] | Shyamsunder, S.Bhatter, K.Jangid, and S. D.Purohit, A study of the hepatitis B virus infection using Hilfer fractional derivative, PIMM48 (2022), 100-117. · Zbl 1519.92305 |
| [7] | S.Bhatter, A.Mathur, D.Kumar, and J.Singh, On certain new results of fractional calculus involving product of generalized special functions, Int. J. Appl. Comput. Math.8 (2022), no. 3, 1-9. · Zbl 1492.26005 |
| [8] | S. D.Purohit, D.Baleanu, and K.Jangid, On the solutions for generalised multiorder fractional partial differential equations arising in physics, Math. Meth. Appl. Sci.46 (2023), 8139-8147. · Zbl 1532.35492 |
| [9] | M. M.Raja, V.Vijayakumar, A.Shukla, K. S.Nisar, and H. M.Baskonus, On the approximate controllability results for fractional integrodifferential systems of order [( 1<r<2 \]\) with sectorial operators, J. Comput. Appl. Math.2022 (2022), 114492. · Zbl 1492.93024 |
| [10] | K.Karthikeyan, P.Karthikeyan, H. M.Baskonus, K.Venkatachalam, and Y.‐M.Chu, Almost sectorial operators on [( \psi \]\)‐Hilfer derivative fractional impulsive integro‐differential equations, Math. Methods Appl. Sci.45 (2021), no. 13, 8045-8059. · Zbl 1532.34075 |
| [11] | K.Jangid, S.Bhatter, S.Meena, and S. D.Purohit, Certain classes of the incomplete I‐functions and their properties, Discontin. Nonlinearity Complex.12 (2023), no. 2, 437-454. |
| [12] | K.Jangid, S. D.Purohit, K. S.Nisar, and T.Shefeeq, The internal blood pressure equation involving incomplete I‐functions, Inf. Sci. Lett.9 (2020), no. 3, 2. |
| [13] | J. V. C.Sousa and E. C.de Oliveira, Two new fractional derivatives of variable order with non‐singular kernel and fractional differential equation, Comp. Appl. Math.37 (2018), no. 4, 5375-5394. · Zbl 1401.26016 |
| [14] | D.Baleanu, S.Etemad, S.Pourrazi, and S.Rezapour, On the new fractional hybrid boundary value problems with three‐point integral hybrid conditions, Adv. Differ. Equ.2019 (2019), no. 1, 1-21. · Zbl 1487.34008 |
| [15] | S. D.Purohit, A. M.Khan, D. L.Suthar, and S.Dave, The impact on raise of environmental pollution and occurrence in biological populations pertaining to incomplete H‐function, Natl. Acad. Sci. Lett.44 (2021), no. 3, 263-266. |
| [16] | J. V. C.Sousa and E. C.De Oliveira, Leibniz type rule: [( \psi \]\)‐Hilfer fractional operator, Commun. Nonlinear Sci. Numer. Simul.77 (2019), 305-311. · Zbl 1477.26012 |
| [17] | A.Atangana and D.Baleanu, New fractional derivatives with nonlocal and non‐singular kernel: theory and application to heat transfer model, 2016. arXiv preprint arXiv:1602.03408. |
| [18] | K.Jangid, S.Meena, S.Bhatter, and S. D.Purohit, Generalization of fractional kinetic equations containing incomplete I‐functions, Handbook of fractional calculus for engineering and science, Chapman and Hall/CRC, 2022, pp. 169-185. |
| [19] | S.Bhatter, K.Jangid, S.Kumawat, D.Baleanu, D. L.Suthar, and S. D.Purohit, Analysis of the family of integral equation involving incomplete types of I and [( ‾{I} \]\)‐functions, Appl. Math. Sci. Eng. (AMSE)31 (2023), no. 1, 2165280. |
| [20] | M. A.Chaudhry and S. M.Zubair, On a class of incomplete gamma functions with applications, Chapman and Hall/CRC, 2001. |
| [21] | A. K.Rathie, A new generalization of generalized hypergeometric functions, Le Math.LII (1997), 297-310. · Zbl 0946.33011 |
| [22] | A. K.Rathie, A new generalization of generalized hypergeometric functions, Le Math. (2012). arXiv preprint arXiv:1206.0350. |
| [23] | S.Bhatter, K.Jangid, S.Meena, and S. D.Purohit, Certain integral formulae involving incomplete I‐functions, Science & Technology Asia2021 (2021), 84-95. |
| [24] | K.Jangid, S.Bhatter, S.Meena, D.Baleanu, A. M.Qurashi, and S. D.Purohit, Some fractional calculus findings associated with the incomplete I‐functions, Adv. Differ. Equ.2020 (2020), no. 1, 1-24. · Zbl 1482.26009 |
| [25] | H. M.Srivastava, R. K.Saxena, and R. K.Parmar, Some families of the incomplete H‐functions and the incomplete [( H \]\)‐functions and associated integral transforms and operators of fractional calculus with applications, Russ. J. Math. Phys.25 (2018), no. 1, 116-138. · Zbl 1392.33008 |
| [26] | H. M.Srivastava, K. C.Gupta, and S. P.Goyal, The H‐functions of one and two variables, with applications, South Asian Publishers, 1982. · Zbl 0506.33007 |
| [27] | A. M.Mathai, R. K.Saxena, and H. J.Haubold, The H‐function: theory and applications, Springer Science & Business Media, 2009. |
| [28] | A. A.Kilbas, H. M.Srivastava, and J. J.Trujillo, Theory and applications of fractional differential equations, Vol. 204, Elsevier, 2006. · Zbl 1092.45003 |
| [29] | R.Bellman and R. S.Roth, The Laplace transform, Vol. 3, World Scientific, 1984. · Zbl 1522.44001 |
| [30] | G. A. R. G.Mridula, P.Manohar, L.Chanchalani, and A. L. H. A.Subhash, On generalized composite fractional derivative, WJST11 (2014), no. 12, 1069-1076. |
| [31] | R.Hilfer, Applications of fractional calculus in physics, World scientific, Singapore, 2000. · Zbl 0998.26002 |
| [32] | K. S.Miller and B.Ross, An introduction to the fractional calculus and fractional differential equations, Wiley, New Jersey, U.S., 1993. · Zbl 0789.26002 |
| [33] | M. K.Bansal, S.Lal, D.Kumar, S.Kumar, and J.Singh, Fractional differential equation pertaining to an integral operator involving incomplete H‐function in the kernel, Math. Methods Appl. Sci. (2020), 1-12. |
| [34] | H. M.Srivastava, P.Harjule, and R.Jain, A general fractional differential equation associated with an integral operator with the H‐function in the kernel, Russ. J. Math. Phys.22 (2015), no. 1, 112-126. · Zbl 1326.34023 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
