in this paper, a new identification of the lagrange multipliers by means of the sumudu transform, is employed to  btain a quick and accurate solution to the fractional black-scholes equation with the initial condition for a european option pricing problem. undoubtedly this model is the most well known model for pricing financial derivatives. the fractional derivatives is described in caputo sen...

In this paper, the authors introduce a hierarchic fractal model to describe bone hereditariness. Indeed, experimental data of stress relaxation or creep functions obtained by compressive/tensile tests have been proved to be fit by power law with real exponent 0 ⩽ β ⩽1. The rheological behavior of the material has therefore been obtained, using the Boltzmann-Volterra superposition principle, in ...

In this paper, the 1st-level general fractional derivatives of arbitrary order are defined and investigated for first time. We start with a generalization Sonin condition kernels integrals then specify set that satisfy possess an integrable singularity power law type at origin. The integro-differential operators convolution from set. They contain both Riemann–Liouville regularized considered in...

Abstract In this paper, we present the definitions of fractional integrals and derivatives a Pettis integrable function with respect to another function. This concept follows idea Stieltjes-type operators should allow us study using methods known from measure differential equations in abstract spaces. We will show that some well-known properties calculus for space Lebesgue functions also hold t...

A fractional diffusion equation based on Riemann-Liouville fractional derivatives is solved exactly. The initial values are given as fractional integrals. The solution is obtained in terms of H-functions. It differs from the known solution of fractional diffusion equations based on fractional integrals. The solution of fractional diffusion based on a Riemann-Liouville fractional time derivative...

In this article, we investigate the existence and uniqueness of solutions for a nonlinear coupled system Liouville–Caputo type fractional integro-differential equations supplemented with non-local discrete integral boundary conditions. The nonlinearity relies both on unknown functions their derivatives integrals in lower order. consequence is obtained utilizing alternative Leray–Schauder, while...

This paper investigates the companion of Ostrowski's inequality in framework fractal sets. First, a new identity related to local fractional integrals is introduced, serving as foundation for establishing set inequalities applicable functions with generalized $s$-convex and $s$-concave derivatives. An illustrative example presented validate obtained results, demonstrating their accuracy. Additi...

and Applied Analysis 3 Differential calculus Exponent

Fractals are measurable metric sets with non-integer Hausdorff dimensions. If electric and magnetic fields are defined on fractal and do not exist outside of fractal in Euclidean space, then we can use the fractional generalization of the integral Maxwell equations. The fractional integrals are considered as approximations of integrals on fractals. We prove that fractal can be described as a sp...

In this paper, firstly we have established Hermite–Hadamard-Fejér inequality for fractional integrals. Secondly, an integral identity and some HermiteHadamard-Fejér type integral inequalities for the fractional integrals have been obtained. The some results presented here would provide extensions of those given in earlier works. Mathematics Subject Classification (2010): 26A51, 26A33, 26D10.