Discussion on a new tripled system of hybrid type of FDEs with p-Laplacian involving φ-Caputo derivatives

Hamid Beddani, Moustafa Beddani, Mohammad Esmael Samei

Abstract


Our research is about the analysis of  a new type of triple system of hybrid differential equations of fractional order with nonlocal integro multi point boundary conditions, whose results can certainly be useful in solving practical problems. We focus on a mathematical operator called the p-Laplacian and another type of derivative called the φ-Caputo derivative.  The displayed comes about are gotten by the hybrid  Dhage fixed point theorem for a entirety of three operators. A few illustrative illustrations is displayed at the conclusion to appear the pertinence of the gotten comes about. To the leading of our information, this is often the primary time where such issue is considered.

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References


M. I. Abbas, M. A. Ragusa, On the Hybrid Fractional Differential Equations with Fractional Proportional Derivatives of a Function with Respect to a Certain Function, Symmetry 13 (2021), no. 2, 264.

A. Aghajani, E. Pourhadi, J.J. Trujillo, Application of measure of noncompactness to a Cauchy problem for fractional differential equations in Banach spaces, Fractional Calculus and Applied Analysis 16 (2013), 962-977.

O.P. Agrawal, Some generalized fractional calculus operators and their applications in integral equations, Fractional Calculus and Applied Analysis 15 (2012), 700-711.

R. Almeida, A Caputo fractional derivative of a function with respect to another function, Communications in Nonlinear Science and Numerical Simulation 44 (2017), 460-481.

A. Amara, S. Etemad, S. Rezapour, Approximate solutions for a fractional hybrid initial value problem via the Caputo conformable derivative, Advances in Difference Equations 2020 (2020), 608.

P. Amiri, M.E. Samei, Existence of Urysohn and Atangana-Baleanu fractional integral inclusion systems solutions via common fixed point of multi-valued operators, Chaos, Solitons & Fractals 165 (2022), no. 2, 112822.

H. Beddani, M. Beddani, Solvability for a differential systems via Φ-Caputo approach, Journal of Science and Arts 3 (2021), no. 3, 749-762.

H. Beddani, M. Beddani, Z. Dahmani, An existence study for a tripled system with p-Laplacian involving φ-Caputo derivatives, Miskolc Mathematical Notes 56 (2021), no. 2, 1-17.

H. Beddani, Z. Dahmani, Solvability for nonlinear differential problem of Langevin type via ϕ-Caputo approch, European Journal of Mathematics and Applications 1 (2021), 11.

B. Belhadji, J. Alzabut, M.E. Samei, N. Fatima, On the global behaviour of solutions for a delayed viscoelastic type Petrovesky wave equation with p-Laplace and logarithmic source, Mathematics 10 (2022), 4194.

F. Chabanea, M. Benbachir, M. Hachama, M.E. Samei, Existence of positive solutions for p-Laplacian boundary value problems of fractional differential equations, Boundary Value Problems 2022 (2022), 65.

J. Dehong, G. Weigao, A nonlocal boundary value problems for hybrid φ-Caputo fractional integro-differential equations, AIMS Mathematics 5 (2020), no. 6, 7175-7190.

A. Devi, A. Kumar, D. Baleanu, A. Khan, On stability analysis and existence of positive solutions for a general non-linear fractional differential equations, Advances in Difference Equations 2020 (2020), 300.

B.C. Dhage, A fixed point theorem in Banach algebras with applications to functional integral equations, Kyungpook Mathematical Journal 44 (2004), 145-155.

B.C. Dhage, On a Fixed Point Theorem in Banach Algebras with Applications, Applied Mathematics Letters 18 (2005), no. 3, 273-280.

B.C. Dhage, Quadratic Perturbations Of Periodic Boundary Value Problems Of Second Order Ordinary Differential Equations, Differential Equations and Applications 2 (2010), no. 4, 465-486.

K. Diethelm, The Analysis of Fractional Differential Equations: An Application-oriented Exposition Using Differential Operators of Caputo Type, Springer-Verlag, Berlin, 2010.

S. Etemad, S. Rezapour, M.E. Samei, On fractional hybrid and non-hybrid multi-term integro-differential inclusions with three-point integral hybrid boundary conditions, Advances in Difference Equations 2020 (2020), 161.

S. Ferraoun, Z. Dahmani, Existence and stability of solutions of a class of hybrid fractional differential equations involving RL-operator, Journal of Interdisciplinary Mathematics 23 (2020), no. 4, 885-903.

H.A. Hammad, R.A. Rashwan, A. Nafea, M.E. Samei, M. De la Sen, Stability and existence of solutions for a tripled problem of fractional hybrid delay differential equations, Symmetry 14, no. 12, (2022), 2579.

R. Herrmann, Fractional Calculus for Physicist, World Scientific, Berlin, 2014.

M.D. Kassim, N.E. Tatar, Stability of logarithmic type for a Hadamard fractional differential problem, Journal of Pseudo-Differential Operators and Applications 11 (2020), 447-466.

H. Khan, T. Abdeljawad, M. Aslam, R.A. Khan, A. Khan, Existence of positive solution and Hyers-Ulam stability for a nonlinear singular-delay-fractional differential equation, Advances in Difference Equations 2019 (2019), 104.

H. Khan, W. Chen, H. Sun, Analysis of positive solution and Hyers-Ulam stability for a class of singular fractional differential equations with p-Laplacian in Banach space, Mathematical Methods in the Applied Sciences 41 (2018), no. 9, 3430-3440.

A. Khan, M.I. Syam, A. Zada, H. Khan, Stability analysis of nonlinear fractional differential equations with Caputo and Riemann-Liouville derivatives, The European Physical Journal Plus 133 (2018), 264.

A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier Science, North-Holland Mathematics Studies, Amsterdam, 2006.

Y. Li, Existence of positive solutions for fractional differential equation involving integral boundary conditions with p-Laplacian operator, Advances in Difference Equations 2017 (2017), no. 2, 135.

T.J. Osler, Fractional derivatives of a composite function, SIAM Journal on Mathematical Analysis 1 (1970), no. 2, 288-293.

A. Parvate, A.D. Gangal, Fractal differential equations and fractal-time dynamical systems, Pramana 64 (2005), 389-409.

I. Podlubny, Fractional Differential Equations, Academic Press, New York, 1993.

H. Qin, X. Zuo, J. Liu, Existence and controllability results for fractional impulsive integro-differential systems in Banach spaces, Abstract and Applied Analysis 2013 (2013), no. 295837, 12 pages.

S.G. Samko, A.A. Kilbas, O.I. Marichev, Fractional Integrals and Derivatives: Theory and Applications, Gordon and Breach Science Publishers, Switzerland; Philadelphia, USA, 1993.

A. Seemab, M.U. Rehman, J. Alzabut, M. Rehman, Y. Adjabi, M.S. Abdo, Langevin equation with nonlocal boundary conditions involving a 􀀀Caputo fractional operator, AIMS Mathematics 6 (2021), no. 7, 6749-6780.

Y. Wang, Existence and nonexistence of positive solutions for mixed fractional boundary value problem with parameter and p-Laplacian operator, Journal of Function Spaces 62 (2018), no. 1462825, 6 pages.

Y. Zhao, S. Sun, Z. Han, Q. Li, Theory of fractional hybrid differential equations, Computers & Mathematics with Applications 62 (2011), no. 3, 1312-1324.

A. Boutiara, M.M. Matar, J. Alzabut, M.E. Samei, H. Khan, Investigation of ABC coupled Langevin fractional differential equations constrained by Perov's fixed point in generalized Banach spaces, AIMS Mathematics 8 (2023), no. 5, 12109-12132.




DOI: https://doi.org/10.52846/ami.v52i2.1982