On solution of non-instantaneous impulsive Hilfer fractional integro-differential evolution system

• Autorzy: Trivedi Gargi J. , Shah Vishant , Sharma Jaita , Sanghvi Rajesh

Identyfikatory

DOI

10.14708/ma.v51i1.7167

Warianty tytułu

PL

O rozwiązaniu impulsowego ulamkowego układu całkowo-różnicowego Hilfera z opóźnieniem

• Języki publikacji: EN

Abstrakty

EN

In this article, we have considered the non-instantaneous fractional integrodifferential evolution system with Hilfer fractional differential operator in the Banach space and discussed its existence results for the mild solution for the equation with local and non-local conditions. These results are obtained by applying the method of a C0 operator generated by the linear part of the equation combined with the concept of nonlinear functional analysis and the fixed point theorems. We have discussed the examples to highlight the applicability of the results.

PL

Artykuł poświęcony jest ułamkowym, z opóźnieniem, systemom ewolucji całkowo-różniczkowej opisanym ułamkowym operatorem różniczkowym Hilfera w przestrzeni Banacha. Analizowane jest istnienia gładkiego rozwiązania równania z warunkami lokalnymi i nielokalnymi. Wyniki uzyskano stosując do operatora C0 generowanego przez liniową część równania metody nieliniowej analizy funkcjonalnej z twierdzeniami o punkcie stałym. Zamieszczone przykłady podkreślają znaczenie otrzymanych wyników.

Słowa kluczowe

EN

fractional evolution equation; Hilfer fractional differential operator; operator semigroup; non-instantaneous impulses; fixed point theorem

PL

ułamkowe równanie ewolucji; ułamkowy operator różniczkowy Hilfera; półgrupa operatorów; impulsy opóźnione; twierdzenie o punkcie stałym

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Mathematica Applicanda
• Rocznik: 2023
• Tom: Vol. 51, no. 1
• Strony: 33--50
• Opis fizyczny: Bibliogr. 14 poz.

Twórcy

autor

Trivedi Gargi J.

• Charutar Vidya Mandal University Department of Mathematics G. H. Patel College of Engineering and Technology CVM University, Vallabh Vidhyanagar - Anand, Gujarat 388120, India

• https://orcid.org/0000-0001-6597-1420

autor

Shah Vishant

• The M. S. University of Baroda, Vadodara The M. S. University of Baroda, Vadodara Pratapgunj, Vadodara, Gujarat 390002, Indie

• https://orcid.org/0000-0003-3168-652X

autor

Sharma Jaita

• The Maharaja Sayajirao University of Baroda The M. S. University of Baroda Pratapgunj, Vadodara, Gujarat 390002, Indie

• https://orcid.org/0000-0002-9445-0912

autor

Sanghvi Rajesh

• Charutar Vidya Mandal University Department of Mathematics G. H. Patel College of Engineering and Technology CVM University, Vallabh Vidhyanagar, Gujarat 388120, India

• https://orcid.org/0000-0003-2624-0558

Bibliografia

• [1] S. Ahmad, A. Ullah, Q. M. Al-Mdallal, H. Khan, K. Shah, and A. Khan. Fractional order mathematical modeling of covid-19 transmission. Chaos, Solitons & Fractals, 139:110256, 10 2020. ISSN 09600779. doi:10.1016/j.chaos.2020.110256.
• [2] J. Borah and S. N. Bora. Existence of mild solution of a class of nonlocal fractional order differential equation with not instantaneous impulses. Fractional Calculus and Applied Analysis, 22:495–508, 4 2019. ISSN 1311-0454. doi: 10.1515/fca-2019-0029.
• [3] M. M. El-Borai. Some probability densities and fundamental solutions of fractional evolution equations. Chaos, Solitons & Fractals, 14:433-440, 8 2002. ISSN 09600779. doi: 10.1016/S0960- 0779(01)00208-9.
• [4] M. M. El-Borai. Semigroups and some nonlinear fractional differential equations. Applied Mathematics and Computation, 149:823-831, 2 2004. ISSN 00963003. doi: 10.1016/S0096-3003(03)00188-7.
• [5] M. Fe£kan, J.-R. Wang, and Y. Zhou. On the new concept of solutions and existence results for impulsive fractional evolution equations. Dynamics of Partial Differential Equations, 8:345 361, 2011. ISSN 1548159X. doi: 10.4310/DPDE.2011.v8.n4.a3.
• [6] R. Hilfer, editor. Applications of fractional calculus in physics. Singapore: World Scienti c, 2000. ISBN 981-02-3457-0. Zbl 0998.26002. Cited on p. 3. [7] A. Jaiswal and D. Bahuguna. Hilfer fractional differential equations with almost sectorial operators. Differential Equations and Dynamical Systems, 1 2020. ISSN 0971-3514. doi: 10.1007/s12591-020-00514-y.
• [7] H. Kataria and P. Patel. Existence and uniqueness of non-local cauchy problem for fractional differential equation on banach space. International Journal of Pure and Applied Mathematics, 120:10237, 07 2018. ISSN 10237-10252.
• [8] H. R. Kataria and P. H. Patel. Congruency between classical and mild solutions of caputo fractional impulsive evolution equation on Banach space. International Journal of Advanced Science and Technology, 29: 1923 1936, 2020. ISSN 2005-4238.
• [9] H. R. Kataria, P. H. Patel, and V. Shah. Existence results of noninstantaneous impulsive fractional integro-differential equation. Demonstratio Mathematica, 53:373-384, 12 2020. ISSN 2391-4661. doi: 10.1515/dema2020-0029.
• [10] A. Meraj and D. N. Pandey. Existence of mild solutions for fractional non-instantaneous impulsive integro-differential equations with nonlocal conditions. Arab Journal of Mathematical Sciences, 26:3-13, 8 2020. ISSN 1319-5166. doi: 10.1016/j.ajmsc.2018.11.002.
• [11] K. S. Miller and B. Ross. An introduction to the fractional calculus and fractional differential equations. A Wiley-Interscience Publication. John Wiley & Sons, Inc., New York, 1993. ISBN 0-471-58884-9.
• [12] I. Podlubny. Fractional differential equations, volume 198 of Mathematics in Science and Engineering. Academic Press, Inc., San Diego, CA, 1999. ISBN 0-12-558840-2. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications. MR 1658022.
• [13] V. Shah, R. K. George, J. Sharma, and P. Muthukumar. Existence and uniqueness of classical and mild solutions of generalized impulsive evolution equation. International Journal of Nonlinear Sciences and Numerical Simulation, 19:775-780, 12 2018.
• [14] C.-J. Xu and P.-L. Li. Mild solution of fractional order differential equations with not instantaneous impulses. Open Mathematics, 13:null, 2015. URL http://eudml.org/doc/271049.

Uwagi

PL

Opracowane ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).