Abstract
This article concerns with the existence and uniqueness theory of solutions for sequential fractional differential system involving Caputo fractional derivatives of order 1<alpha, beta<2 with coupled nonseparated boundary conditions. The standard tools of the fixed point theory were used to establish the main results. Application is introduced to show the validity of our results.
Highlights
PreliminariesSome definitions of fractional are introduced as they are required in sequel of this study
E studied equation, equation (1), is subject to boundary conditions which are coupled but nonseparated. e main goal of the article is to prove the existence of solutions to the problem defined by equation (1). e theory of fractional differential equation subject to boundary conditions has long been of the interest of researchers
Differential equations with nonlocal boundary conditions are of high importance in applied sciences. ey are useful in modeling some chemical processes and in general to model a process which is located inside a defined region
Summary
Some definitions of fractional are introduced as they are required in sequel of this study. Consider a real number c > 0; the Mittag–Leffler function with one parameter is computed as. + 1), where x ∈ tsr− 1ds, ∀r > 0. Definition 2 (see [15]). Given α ∈ R+ demonstrating the order of the derivative, the Caputo fractional derivative of order α of a function φ: [0, +∞] ⟶ R is given by.
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