A Study of Nonlinear Fractional Differential Equations of Arbitrary Order with Riemann-Liouville Type Multistrip Boundary Conditions

Abstract

We develop the existence theory for nonlinear fractional differential equations of arbitrary order with Riemann-Liouville type boundary conditions involving nonintersecting finite many strips of arbitrary length. Our results are based on some standard tools of fixed point theory. For the illustration of the results, some examples are also discussed.

Existence and Stability Results for a Fractional Order Differential Equation with Non-Conjugate Riemann-Stieltjes Integro-Multipoint Boundary Conditions

“…The nonlocal boundary conditions are found to be of great utility in modeling the changes happening within the domain of the given scientific phenomena, while the concept of integral boundary conditions is applied to model the physical problems, such as blood flow problems on arbitrary structures and ill-posed backward problems. For some recent works on fractional order differential equations involving Riemann-Liouville, Caputo, and Hadamard type fractional derivatives, equipped with classical, nonlocal, and integral boundary conditions, we refer the reader to a series of papers [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28] and the references cited therein.…”

Some Existence Results For Higher Order Fractional Differential Equations with Multi-Strip Riemann-Liouville Type Fractional Integral Boundary Conditions

“…η m < 1 and γ i ∈ R are appropriately chosen constants. The strip boundary condition in problem (1) can be regarded as a Riemann-Liouville type fractional integral boundary conditions involving non-intersecting finite many strips of arbitrary length, for example, see [5,7,20]. The paper is organized as follows: In Sec.…”

Coupled systems of Riemann-Liouville fractional differential equations with Hadamard fractional integral boundary conditions

“…Fractional calculus has also emerged as a powerful modeling tool for many real world problems. For examples and recent development of the topic, see ( [1,2,3,4,5,6,7,14,16,17,18,19,20]). However, it has been observed that most of the work on the topic involves either Riemann-Liouville or Caputo type fractional derivatve.…”