Existence and Uniqueness Solutions of System Caputo-Type Fractional-Order Boundary Value Problems using Monotone Iterative Method

Audubmbar Kumar Mule; Sidheshwar S. Bellale

doi:https://doi.org/10.14445/22315373/IJMTT-V69I6P507

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 69 | Issue 6 | Year 2023 | Article Id. IJMTT-V69I6P507 | DOI : https://doi.org/10.14445/22315373/IJMTT-V69I6P507

Existence and Uniqueness Solutions of System Caputo-Type Fractional-Order Boundary Value Problems using Monotone Iterative Method

Audubmbar Kumar Mule, Sidheshwar S. Bellale

Received	Revised	Accepted	Published
21 Apr 2023	28 May 2023	13 Jun 2023	23 Jun 2023

Abstract

In this paper, we investigate the existence and uniqueness solutions of nonlinear boundary value problems for a system of Caputo-type nonlinear fractional differential equations of the form: {cDa+q;Ψui(t) = Fi(t, u1(t), u2(t)) t ε J = [a,b], Φ(vi(a), vi(b)) = 0. To develop a monotone iterative technique by introducing upper and lower solutions to Caputo-type fractional differential equations with nonlinear boundary conditions. The monotone method yields monotone sequences which converge uniformly and monotonically to extremal solutions.

Keywords

Ψ-Caputo fractional derivative, Upper and lower solutions, Monotone iterative method.

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Citation :

Audubmbar Kumar Mule, Sidheshwar S. Bellale, "Existence and Uniqueness Solutions of System Caputo-Type Fractional-Order Boundary Value Problems using Monotone Iterative Method," International Journal of Mathematics Trends and Technology (IJMTT), vol. 69, no. 6, pp. 48-58, 2023. Crossref, https://doi.org/10.14445/22315373/IJMTT-V69I6P507