Nonlocal integro-multistrip-multipoint boundary value problems for $ \overline{\psi}_{*} $-Hilfer proportional fractional differential equations and inclusions

Sotiris K. Ntouyas; Bashir Ahmad; Jessada Tariboon; Sotiris K. Ntouyas; Bashir Ahmad; Jessada Tariboon

doi:10.3934/math.2023720

AIMS Mathematics

2023, Volume 8, Issue 6: 14086-14110. doi: 10.3934/math.2023720

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Research article

Nonlocal integro-multistrip-multipoint boundary value problems for $ \overline{\psi}_{*} $-Hilfer proportional fractional differential equations and inclusions

1.
Department of Mathematics, University of Ioannina, Ioannina 45110, Greece
2.
Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia
3.
Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok 10800, Thailand

Received: 12 February 2023 Revised: 27 March 2023 Accepted: 02 April 2023 Published: 14 April 2023
MSC : 26A33, 34A08, 34A60, 34B15

In the present paper, we establish the existence criteria for solutions of single valued and multivalued boundary value problems involving a $ \overline{\psi}_{*} $-Hilfer fractional proportional derivative operator, subject to nonlocal integro-multistrip-multipoint boundary conditions. We apply the fixed-point approach to obtain the desired results for the given problems. The obtained results are well-illustrated by numerical examples. It is important to mention that several new results appear as special cases of the results derived in this paper (for details, see the last section).
Citation: Sotiris K. Ntouyas, Bashir Ahmad, Jessada Tariboon. Nonlocal integro-multistrip-multipoint boundary value problems for $ \overline{\psi}_{*} $-Hilfer proportional fractional differential equations and inclusions[J]. AIMS Mathematics, 2023, 8(6): 14086-14110. doi: 10.3934/math.2023720

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Abstract

In the present paper, we establish the existence criteria for solutions of single valued and multivalued boundary value problems involving a $ \overline{\psi}_{*} $-Hilfer fractional proportional derivative operator, subject to nonlocal integro-multistrip-multipoint boundary conditions. We apply the fixed-point approach to obtain the desired results for the given problems. The obtained results are well-illustrated by numerical examples. It is important to mention that several new results appear as special cases of the results derived in this paper (for details, see the last section).

References

[1]	R. Hilfer, Applications of fractional calculus in physics, World Scientific, 2000.
[2]	A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and applications of the fractional differential equations, Elsevier, 2006.
[3]	K. Diethelm, The analysis of fractional differential equations, Springer Verlag, 2010.
[4]	Y. Zhou, Basic theory of fractional differential equations, World Scientific, 2014.
[5]	B. Ahmad, A. Alsaedi, S. K. Ntouyas, J. Tariboon, Hadamard-type fractional differential equations, inclusions and inequalities, Springer Verlag, 2017.
[6]	F. Jarad, T. Abdeljawad, J. Alzabut, Generalized fractional derivatives generated by a class of local proportional derivatives, Eur. Phys. J. Spec. Top., 226 (2017), 3457–3471. http://doi.org/10.1140/epjst/e2018-00021-7 doi: 10.1140/epjst/e2018-00021-7
[7]	F. Jarad, M. A. Alqudah, T. Abdeljawad, On more general forms of proportional fractional operators, Open Math., 18 (2020), 167–176. http://doi.org/10.1515/math-2020-0014 doi: 10.1515/math-2020-0014
[8]	F. Jarad, T. Abdeljawad, S. Rashid, Z. Hammouch, More properties of the proportional fractional integrals and derivatives of a function with respect to another function, Adv. Differ. Equations, 2020 (2020), 303. http://doi.org/10.1186/s13662-020-02767-x doi: 10.1186/s13662-020-02767-x
[9]	I. Ahmed, P. Kumam, F. Jarad, P. Borisut, W. Jirakitpuwapat, On Hilfer generalized proportional fractional derivative, Adv. Differ. Equations, 2020 (2020), 329. http://doi.org/10.1186/s13662-020-02792-w doi: 10.1186/s13662-020-02792-w
[10]	A. Jajarmi, D. Baleanu, S. S. Sajjadi, J. J. Nieto, Analysis and some applications of a regularized $\overline{\psi}_{}$-Hilfer fractional derivative, J. Comput. Appl. Math., 415* (2022), 114476. http://doi.org/10.1016/j.cam.2022.114476 doi: 10.1016/j.cam.2022.114476
[11]	H. Gu, J. J. Trujillo, Existence of mild solution for evolution equation with Hilfer fractional derivative, Appl. Math. Comput., 257 (2015), 344–354. http://doi.org/10.1016/j.amc.2014.10.083 doi: 10.1016/j.amc.2014.10.083
[12]	J. Wang, Y. Zhang, Nonlocal initial value problems for differential equations with Hilfer fractional derivative, Appl. Math. Comput., 266 (2015), 850–859. http://doi.org/10.1016/j.amc.2015.05.144 doi: 10.1016/j.amc.2015.05.144
[13]	J. V. da C. Sousa, E. C. de Oliveira, On the $\overline{\psi}_{}$-Hilfer fractional derivative, Commun. Nonlinear Sci. Numer. Simul.*, 60 (2018), 72–91. http://doi.org/10.1016/j.cnsns.2018.01.005 doi: 10.1016/j.cnsns.2018.01.005
[14]	S. Asawasamrit, A. Kijjathanakorn, S. K. Ntouyas, J. Tariboon, Nonlocal boundary value problems for Hilfer fractional differential equations, Bull. Korean Math. Soc., 55 (2018), 1639–1657. http://doi.org/10.4134/BKMS.b170887 doi: 10.4134/BKMS.b170887
[15]	B. Ahmad, S. K. Ntouyas, Nonlocal nonlinear fractional-order boundary value problems, World Scientific, 2021. http://doi.org/10.1142/12102
[16]	S. K. Ntouyas, A survey on existence results for boundary value problems of Hilfer fractional differential equations and inclusions, Foundations, 2021 (2021), 63–98. http://doi.org/10.3390/foundations1010007 doi: 10.3390/foundations1010007
[17]	I. Mallah, I. Ahmed, A. Akgul, F. Jarad, S. Alha, On $\overline{\psi}_{}$-Hilfer generalized proportional fractional operators, AIMS Math.*, 7 (2021), 82–103. http://doi.org/10.3934/math.2022005 doi: 10.3934/math.2022005
[18]	S. K. Ntouyas, B. Ahmad, J. Tariboon, Nonlocal $\overline{\psi}_{}$-Hilfer generalized proportional boundary value problems for fractional differential equations and inclusions, Foundations, 2022* (2022), 377–398. http://doi.org/10.3390/foundations2020026 doi: 10.3390/foundations2020026
[19]	K. Deimling, Nonlinear functional analysis, Springer Verlag, 1985.
[20]	M. A. Krasnosel'ski${\rm{\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\smile$}} \over i} }}$, Two remarks on the method of successive approximations, Usp. Mat. Nauk, 10 (1955), 123–127.
[21]	D. R. Smart, Fixed point theory, Cambridge University Press, 1974.
[22]	A. Granas, J. Dugundji, Fixe point theory, Springer Verlag, 2003.
[23]	K. Deimling, Multivalued differential equations, De Gruyter, 1992.
[24]	L. Górniewicz, Topological fixed point theory of multivalued mappings, Kluwer Academic Publishers, 1999.
[25]	S. Hu, N. Papageorgiou, Handbook of multivalued analysis, Kluwer Academic Publishers, 1997.
[26]	A. Lasota, Z. Opial, An application of the Kakutani-Ky Fan theorem in the theory of ordinary differential equations, Bull. Acad. Pol. Sci. Ser. Sci. Math. Astronom. Phys., 13 (1955), 781–786.
[27]	H. Covitz, S. B. Nadler, Multi-valued contraction mappings in generalized metric spaces, Isr. J. Math., 8 (1970), 5–11. http://doi.org/10.1007/BF02771543 doi: 10.1007/BF02771543
[28]	M. Kisielewicz, Differential inclusions and optimal control, Springer Verlag, 1991.
[29]	C. Castaing, M. Valadier, Convex analysis and measurable multifunctions, Springer Verlag, 1977. http://doi.org/10.1007/BFb0087685

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